question stringlengths 286 292 | answer stringclasses 93
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Below are definitions of new mathematical operators.
Definitions:
a ⊞ b = 2*a - 1*b
Compute step by step: 8 ⊞ 1
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 15 | 2 | {"operators": [{"symbol": "⊞", "template_idx": 1, "coeffs": [2, 1]}], "expression_tree": {"type": "op", "symbol": "⊞", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 1}}, "expected_steps": [{"expr_str": "8 ⊞ 1", "result": 15}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊖ b = 1*a + 3*b + 2
Compute step by step: 2 ⊖ 1
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 7 | 2 | {"operators": [{"symbol": "⊖", "template_idx": 0, "coeffs": [1, 3, 2]}], "expression_tree": {"type": "op", "symbol": "⊖", "left": {"type": "leaf", "value": 2}, "right": {"type": "leaf", "value": 1}}, "expected_steps": [{"expr_str": "2 ⊖ 1", "result": 7}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊗ b = 3*a - 3*b
Compute step by step: 4 ⊗ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -9 | 2 | {"operators": [{"symbol": "⊗", "template_idx": 1, "coeffs": [3, 3]}], "expression_tree": {"type": "op", "symbol": "⊗", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "4 ⊗ 7", "result": -9}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 2*a - 2*b
Compute step by step: 8 ⊡ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 4 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "8 ⊡ 6", "result": 4}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊗ b = 2*a - 3*b
Compute step by step: 6 ⊗ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 6 | 2 | {"operators": [{"symbol": "⊗", "template_idx": 1, "coeffs": [2, 3]}], "expression_tree": {"type": "op", "symbol": "⊗", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "6 ⊗ 2", "result": 6}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 2*a + 2*b + 2
Compute step by step: 11 ⊡ 9
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 42 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 0, "coeffs": [2, 2, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 11}, "right": {"type": "leaf", "value": 9}}, "expected_steps": [{"expr_str": "11 ⊡ 9", "result": 42}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊖ b = 3*a + 2*b + 3
Compute step by step: 10 ⊖ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 37 | 2 | {"operators": [{"symbol": "⊖", "template_idx": 0, "coeffs": [3, 2, 3]}], "expression_tree": {"type": "op", "symbol": "⊖", "left": {"type": "leaf", "value": 10}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "10 ⊖ 2", "result": 37}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 2*a - 2*b
Compute step by step: 9 ⊙ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 6 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 9}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "9 ⊙ 6", "result": 6}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 2*a - 1*b
Compute step by step: 8 ⊛ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 9 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 1, "coeffs": [2, 1]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "8 ⊛ 7", "result": 9}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 3*a - 1*b
Compute step by step: 3 ⊘ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 3 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 1, "coeffs": [3, 1]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "3 ⊘ 6", "result": 3}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 2*a + 2*b + 1
Compute step by step: 10 ⊙ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 43 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 0, "coeffs": [2, 2, 1]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 10}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "10 ⊙ 11", "result": 43}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊜ b = 1*a - 3*b
Compute step by step: 3 ⊜ 5
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -12 | 2 | {"operators": [{"symbol": "⊜", "template_idx": 1, "coeffs": [1, 3]}], "expression_tree": {"type": "op", "symbol": "⊜", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 5}}, "expected_steps": [{"expr_str": "3 ⊜ 5", "result": -12}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 1*a - 1*b
Compute step by step: 3 ⊕ 12
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -9 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [1, 1]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 12}}, "expected_steps": [{"expr_str": "3 ⊕ 12", "result": -9}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊜ b = 2*a - 2*b
Compute step by step: 3 ⊜ 5
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -4 | 2 | {"operators": [{"symbol": "⊜", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊜", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 5}}, "expected_steps": [{"expr_str": "3 ⊜ 5", "result": -4}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 3*a - 2*b
Compute step by step: 11 ⊙ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 29 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 1, "coeffs": [3, 2]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 11}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "11 ⊙ 2", "result": 29}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 2*a - 2*b
Compute step by step: 9 ⊕ 3
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 12 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 9}, "right": {"type": "leaf", "value": 3}}, "expected_steps": [{"expr_str": "9 ⊕ 3", "result": 12}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊞ b = 1*a + 2*b + 1
Compute step by step: 6 ⊞ 3
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 13 | 2 | {"operators": [{"symbol": "⊞", "template_idx": 0, "coeffs": [1, 2, 1]}], "expression_tree": {"type": "op", "symbol": "⊞", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 3}}, "expected_steps": [{"expr_str": "6 ⊞ 3", "result": 13}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 1*a + 1*b + 1
Compute step by step: 10 ⊕ 4
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 15 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 0, "coeffs": [1, 1, 1]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 10}, "right": {"type": "leaf", "value": 4}}, "expected_steps": [{"expr_str": "10 ⊕ 4", "result": 15}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 1*a + 2*b + 1
Compute step by step: 3 ⊕ 5
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 14 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 0, "coeffs": [1, 2, 1]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 5}}, "expected_steps": [{"expr_str": "3 ⊕ 5", "result": 14}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 1*a + 1*b + 2
Compute step by step: 1 ⊠ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 5 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 0, "coeffs": [1, 1, 2]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "1 ⊠ 2", "result": 5}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊖ b = 3*a - 3*b
Compute step by step: 4 ⊖ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -6 | 2 | {"operators": [{"symbol": "⊖", "template_idx": 1, "coeffs": [3, 3]}], "expression_tree": {"type": "op", "symbol": "⊖", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "4 ⊖ 6", "result": -6}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 1*a + 1*b + 2
Compute step by step: 6 ⊠ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 16 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 0, "coeffs": [1, 1, 2]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "6 ⊠ 8", "result": 16}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 1*a - 3*b
Compute step by step: 10 ⊙ 9
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -17 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 1, "coeffs": [1, 3]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 10}, "right": {"type": "leaf", "value": 9}}, "expected_steps": [{"expr_str": "10 ⊙ 9", "result": -17}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 3*a + 1*b + 2
Compute step by step: 5 ⊡ 3
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 20 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 0, "coeffs": [3, 1, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 5}, "right": {"type": "leaf", "value": 3}}, "expected_steps": [{"expr_str": "5 ⊡ 3", "result": 20}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 1*a + 1*b + 2
Compute step by step: 5 ⊛ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 18 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 0, "coeffs": [1, 1, 2]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 5}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "5 ⊛ 11", "result": 18}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 2*a + 1*b + 1
Compute step by step: 1 ⊠ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 13 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 0, "coeffs": [2, 1, 1]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "1 ⊠ 10", "result": 13}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊜ b = 1*a - 2*b
Compute step by step: 11 ⊜ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 7 | 2 | {"operators": [{"symbol": "⊜", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊜", "left": {"type": "leaf", "value": 11}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "11 ⊜ 2", "result": 7}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 2*a + 3*b + 1
Compute step by step: 3 ⊙ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 31 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 0, "coeffs": [2, 3, 1]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "3 ⊙ 8", "result": 31}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 1*a - 2*b
Compute step by step: 9 ⊡ 12
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -15 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 9}, "right": {"type": "leaf", "value": 12}}, "expected_steps": [{"expr_str": "9 ⊡ 12", "result": -15}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊞ b = 1*a - 2*b
Compute step by step: 6 ⊞ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -8 | 2 | {"operators": [{"symbol": "⊞", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊞", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "6 ⊞ 7", "result": -8}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊖ b = 3*a - 2*b
Compute step by step: 8 ⊖ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 10 | 2 | {"operators": [{"symbol": "⊖", "template_idx": 1, "coeffs": [3, 2]}], "expression_tree": {"type": "op", "symbol": "⊖", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "8 ⊖ 7", "result": 10}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊖ b = 3*a - 3*b
Compute step by step: 2 ⊖ 3
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -3 | 2 | {"operators": [{"symbol": "⊖", "template_idx": 1, "coeffs": [3, 3]}], "expression_tree": {"type": "op", "symbol": "⊖", "left": {"type": "leaf", "value": 2}, "right": {"type": "leaf", "value": 3}}, "expected_steps": [{"expr_str": "2 ⊖ 3", "result": -3}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊞ b = 1*a - 2*b
Compute step by step: 2 ⊞ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -18 | 2 | {"operators": [{"symbol": "⊞", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊞", "left": {"type": "leaf", "value": 2}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "2 ⊞ 10", "result": -18}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊗ b = 2*a - 2*b
Compute step by step: 6 ⊗ 4
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 4 | 2 | {"operators": [{"symbol": "⊗", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊗", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 4}}, "expected_steps": [{"expr_str": "6 ⊗ 4", "result": 4}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 1*a - 3*b
Compute step by step: 12 ⊕ 5
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -3 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [1, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 5}}, "expected_steps": [{"expr_str": "12 ⊕ 5", "result": -3}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊖ b = 1*a - 1*b
Compute step by step: 12 ⊖ 9
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 3 | 2 | {"operators": [{"symbol": "⊖", "template_idx": 1, "coeffs": [1, 1]}], "expression_tree": {"type": "op", "symbol": "⊖", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 9}}, "expected_steps": [{"expr_str": "12 ⊖ 9", "result": 3}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 3*a - 3*b
Compute step by step: 3 ⊕ 12
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -27 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [3, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 12}}, "expected_steps": [{"expr_str": "3 ⊕ 12", "result": -27}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 1*a - 2*b
Compute step by step: 10 ⊡ 5
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 0 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 10}, "right": {"type": "leaf", "value": 5}}, "expected_steps": [{"expr_str": "10 ⊡ 5", "result": 0}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 1*a - 3*b
Compute step by step: 1 ⊕ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -23 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [1, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "1 ⊕ 8", "result": -23}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊜ b = 3*a + 2*b + 2
Compute step by step: 11 ⊜ 4
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 43 | 2 | {"operators": [{"symbol": "⊜", "template_idx": 0, "coeffs": [3, 2, 2]}], "expression_tree": {"type": "op", "symbol": "⊜", "left": {"type": "leaf", "value": 11}, "right": {"type": "leaf", "value": 4}}, "expected_steps": [{"expr_str": "11 ⊜ 4", "result": 43}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 3*a - 2*b
Compute step by step: 1 ⊠ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -13 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 1, "coeffs": [3, 2]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "1 ⊠ 8", "result": -13}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 1*a - 3*b
Compute step by step: 2 ⊠ 12
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -34 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 1, "coeffs": [1, 3]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 2}, "right": {"type": "leaf", "value": 12}}, "expected_steps": [{"expr_str": "2 ⊠ 12", "result": -34}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 3*a + 3*b + 2
Compute step by step: 7 ⊛ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 56 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 0, "coeffs": [3, 3, 2]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 7}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "7 ⊛ 11", "result": 56}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 1*a - 2*b
Compute step by step: 9 ⊛ 3
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 3 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 9}, "right": {"type": "leaf", "value": 3}}, "expected_steps": [{"expr_str": "9 ⊛ 3", "result": 3}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 1*a - 3*b
Compute step by step: 4 ⊕ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -17 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [1, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "4 ⊕ 7", "result": -17}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊗ b = 1*a + 3*b + 2
Compute step by step: 7 ⊗ 3
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 18 | 2 | {"operators": [{"symbol": "⊗", "template_idx": 0, "coeffs": [1, 3, 2]}], "expression_tree": {"type": "op", "symbol": "⊗", "left": {"type": "leaf", "value": 7}, "right": {"type": "leaf", "value": 3}}, "expected_steps": [{"expr_str": "7 ⊗ 3", "result": 18}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 2*a - 2*b
Compute step by step: 3 ⊘ 1
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 4 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 1}}, "expected_steps": [{"expr_str": "3 ⊘ 1", "result": 4}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 2*a - 3*b
Compute step by step: 3 ⊕ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -18 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [2, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "3 ⊕ 8", "result": -18}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 1*a - 1*b
Compute step by step: 6 ⊡ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -5 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [1, 1]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "6 ⊡ 11", "result": -5}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 2*a - 1*b
Compute step by step: 10 ⊛ 1
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 19 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 1, "coeffs": [2, 1]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 10}, "right": {"type": "leaf", "value": 1}}, "expected_steps": [{"expr_str": "10 ⊛ 1", "result": 19}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 2*a - 3*b
Compute step by step: 1 ⊘ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -19 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 1, "coeffs": [2, 3]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "1 ⊘ 7", "result": -19}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 3*a - 1*b
Compute step by step: 4 ⊡ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 5 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [3, 1]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "4 ⊡ 7", "result": 5}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 3*a + 2*b + 1
Compute step by step: 8 ⊙ 9
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 43 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 0, "coeffs": [3, 2, 1]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 9}}, "expected_steps": [{"expr_str": "8 ⊙ 9", "result": 43}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 2*a - 1*b
Compute step by step: 12 ⊘ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 14 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 1, "coeffs": [2, 1]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "12 ⊘ 10", "result": 14}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 1*a + 1*b + 1
Compute step by step: 10 ⊛ 4
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 15 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 0, "coeffs": [1, 1, 1]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 10}, "right": {"type": "leaf", "value": 4}}, "expected_steps": [{"expr_str": "10 ⊛ 4", "result": 15}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 1*a - 3*b
Compute step by step: 6 ⊕ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -18 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [1, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "6 ⊕ 8", "result": -18}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 1*a - 3*b
Compute step by step: 6 ⊕ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -24 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [1, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "6 ⊕ 10", "result": -24}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊗ b = 1*a - 2*b
Compute step by step: 7 ⊗ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -13 | 2 | {"operators": [{"symbol": "⊗", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊗", "left": {"type": "leaf", "value": 7}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "7 ⊗ 10", "result": -13}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 3*a + 2*b + 3
Compute step by step: 1 ⊘ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 18 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 0, "coeffs": [3, 2, 3]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "1 ⊘ 6", "result": 18}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊜ b = 1*a - 1*b
Compute step by step: 9 ⊜ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 7 | 2 | {"operators": [{"symbol": "⊜", "template_idx": 1, "coeffs": [1, 1]}], "expression_tree": {"type": "op", "symbol": "⊜", "left": {"type": "leaf", "value": 9}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "9 ⊜ 2", "result": 7}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 1*a - 1*b
Compute step by step: 3 ⊠ 12
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -9 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 1, "coeffs": [1, 1]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 12}}, "expected_steps": [{"expr_str": "3 ⊠ 12", "result": -9}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 2*a + 3*b + 1
Compute step by step: 8 ⊕ 9
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 44 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 0, "coeffs": [2, 3, 1]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 9}}, "expected_steps": [{"expr_str": "8 ⊕ 9", "result": 44}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊖ b = 2*a + 2*b + 2
Compute step by step: 3 ⊖ 9
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 26 | 2 | {"operators": [{"symbol": "⊖", "template_idx": 0, "coeffs": [2, 2, 2]}], "expression_tree": {"type": "op", "symbol": "⊖", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 9}}, "expected_steps": [{"expr_str": "3 ⊖ 9", "result": 26}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 2*a - 2*b
Compute step by step: 12 ⊡ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 8 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "12 ⊡ 8", "result": 8}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊗ b = 2*a - 2*b
Compute step by step: 12 ⊗ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 20 | 2 | {"operators": [{"symbol": "⊗", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊗", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "12 ⊗ 2", "result": 20}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 1*a - 2*b
Compute step by step: 12 ⊘ 3
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 6 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 3}}, "expected_steps": [{"expr_str": "12 ⊘ 3", "result": 6}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 2*a - 2*b
Compute step by step: 1 ⊕ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -20 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "1 ⊕ 11", "result": -20}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 3*a - 1*b
Compute step by step: 3 ⊡ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 2 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [3, 1]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "3 ⊡ 7", "result": 2}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊞ b = 2*a - 2*b
Compute step by step: 6 ⊞ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 0 | 2 | {"operators": [{"symbol": "⊞", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊞", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "6 ⊞ 6", "result": 0}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊞ b = 2*a + 2*b + 1
Compute step by step: 12 ⊞ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 47 | 2 | {"operators": [{"symbol": "⊞", "template_idx": 0, "coeffs": [2, 2, 1]}], "expression_tree": {"type": "op", "symbol": "⊞", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "12 ⊞ 11", "result": 47}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 1*a + 1*b + 1
Compute step by step: 2 ⊠ 1
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 4 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 0, "coeffs": [1, 1, 1]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 2}, "right": {"type": "leaf", "value": 1}}, "expected_steps": [{"expr_str": "2 ⊠ 1", "result": 4}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 3*a + 2*b + 3
Compute step by step: 8 ⊕ 3
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 33 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 0, "coeffs": [3, 2, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 3}}, "expected_steps": [{"expr_str": "8 ⊕ 3", "result": 33}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊜ b = 1*a + 3*b + 2
Compute step by step: 5 ⊜ 1
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 10 | 2 | {"operators": [{"symbol": "⊜", "template_idx": 0, "coeffs": [1, 3, 2]}], "expression_tree": {"type": "op", "symbol": "⊜", "left": {"type": "leaf", "value": 5}, "right": {"type": "leaf", "value": 1}}, "expected_steps": [{"expr_str": "5 ⊜ 1", "result": 10}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 2*a - 3*b
Compute step by step: 9 ⊛ 5
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 3 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 1, "coeffs": [2, 3]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 9}, "right": {"type": "leaf", "value": 5}}, "expected_steps": [{"expr_str": "9 ⊛ 5", "result": 3}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 1*a + 2*b + 3
Compute step by step: 3 ⊠ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 22 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 0, "coeffs": [1, 2, 3]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "3 ⊠ 8", "result": 22}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 2*a - 1*b
Compute step by step: 7 ⊡ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 8 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [2, 1]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 7}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "7 ⊡ 6", "result": 8}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 2*a + 2*b + 2
Compute step by step: 6 ⊕ 5
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 24 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 0, "coeffs": [2, 2, 2]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 6}, "right": {"type": "leaf", "value": 5}}, "expected_steps": [{"expr_str": "6 ⊕ 5", "result": 24}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 3*a + 1*b + 2
Compute step by step: 8 ⊡ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 33 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 0, "coeffs": [3, 1, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "8 ⊡ 7", "result": 33}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 2*a - 2*b
Compute step by step: 4 ⊡ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -14 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "4 ⊡ 11", "result": -14}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 1*a - 2*b
Compute step by step: 7 ⊘ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -13 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 7}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "7 ⊘ 10", "result": -13}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 2*a + 1*b + 2
Compute step by step: 4 ⊛ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 18 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 0, "coeffs": [2, 1, 2]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "4 ⊛ 8", "result": 18}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 3*a - 2*b
Compute step by step: 12 ⊠ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 14 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 1, "coeffs": [3, 2]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "12 ⊠ 11", "result": 14}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊞ b = 3*a + 2*b + 3
Compute step by step: 2 ⊞ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 29 | 2 | {"operators": [{"symbol": "⊞", "template_idx": 0, "coeffs": [3, 2, 3]}], "expression_tree": {"type": "op", "symbol": "⊞", "left": {"type": "leaf", "value": 2}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "2 ⊞ 10", "result": 29}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 1*a + 1*b + 3
Compute step by step: 3 ⊠ 4
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 10 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 0, "coeffs": [1, 1, 3]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 4}}, "expected_steps": [{"expr_str": "3 ⊠ 4", "result": 10}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 2*a - 1*b
Compute step by step: 1 ⊘ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 0 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 1, "coeffs": [2, 1]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "1 ⊘ 2", "result": 0}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊜ b = 2*a + 2*b + 1
Compute step by step: 12 ⊜ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 37 | 2 | {"operators": [{"symbol": "⊜", "template_idx": 0, "coeffs": [2, 2, 1]}], "expression_tree": {"type": "op", "symbol": "⊜", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "12 ⊜ 6", "result": 37}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 2*a - 2*b
Compute step by step: 5 ⊙ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -6 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 5}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "5 ⊙ 8", "result": -6}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊘ b = 2*a - 3*b
Compute step by step: 10 ⊘ 7
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -1 | 2 | {"operators": [{"symbol": "⊘", "template_idx": 1, "coeffs": [2, 3]}], "expression_tree": {"type": "op", "symbol": "⊘", "left": {"type": "leaf", "value": 10}, "right": {"type": "leaf", "value": 7}}, "expected_steps": [{"expr_str": "10 ⊘ 7", "result": -1}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 2*a + 2*b + 1
Compute step by step: 12 ⊕ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 47 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 0, "coeffs": [2, 2, 1]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "12 ⊕ 11", "result": 47}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 3*a + 2*b + 2
Compute step by step: 2 ⊙ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 24 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 0, "coeffs": [3, 2, 2]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 2}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "2 ⊙ 8", "result": 24}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊗ b = 2*a + 2*b + 2
Compute step by step: 4 ⊗ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 32 | 2 | {"operators": [{"symbol": "⊗", "template_idx": 0, "coeffs": [2, 2, 2]}], "expression_tree": {"type": "op", "symbol": "⊗", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "4 ⊗ 11", "result": 32}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 3*a + 2*b + 1
Compute step by step: 3 ⊕ 6
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 22 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 0, "coeffs": [3, 2, 1]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 3}, "right": {"type": "leaf", "value": 6}}, "expected_steps": [{"expr_str": "3 ⊕ 6", "result": 22}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 2*a - 1*b
Compute step by step: 4 ⊙ 12
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -4 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 1, "coeffs": [2, 1]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 12}}, "expected_steps": [{"expr_str": "4 ⊙ 12", "result": -4}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊠ b = 1*a - 2*b
Compute step by step: 7 ⊠ 2
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 3 | 2 | {"operators": [{"symbol": "⊠", "template_idx": 1, "coeffs": [1, 2]}], "expression_tree": {"type": "op", "symbol": "⊠", "left": {"type": "leaf", "value": 7}, "right": {"type": "leaf", "value": 2}}, "expected_steps": [{"expr_str": "7 ⊠ 2", "result": 3}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊡ b = 2*a - 2*b
Compute step by step: 8 ⊡ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -4 | 2 | {"operators": [{"symbol": "⊡", "template_idx": 1, "coeffs": [2, 2]}], "expression_tree": {"type": "op", "symbol": "⊡", "left": {"type": "leaf", "value": 8}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "8 ⊡ 10", "result": -4}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊜ b = 3*a - 2*b
Compute step by step: 1 ⊜ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | -13 | 2 | {"operators": [{"symbol": "⊜", "template_idx": 1, "coeffs": [3, 2]}], "expression_tree": {"type": "op", "symbol": "⊜", "left": {"type": "leaf", "value": 1}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "1 ⊜ 8", "result": -13}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊙ b = 2*a + 3*b + 1
Compute step by step: 4 ⊙ 11
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 42 | 2 | {"operators": [{"symbol": "⊙", "template_idx": 0, "coeffs": [2, 3, 1]}], "expression_tree": {"type": "op", "symbol": "⊙", "left": {"type": "leaf", "value": 4}, "right": {"type": "leaf", "value": 11}}, "expected_steps": [{"expr_str": "4 ⊙ 11", "result": 42}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊗ b = 3*a - 2*b
Compute step by step: 11 ⊗ 8
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 17 | 2 | {"operators": [{"symbol": "⊗", "template_idx": 1, "coeffs": [3, 2]}], "expression_tree": {"type": "op", "symbol": "⊗", "left": {"type": "leaf", "value": 11}, "right": {"type": "leaf", "value": 8}}, "expected_steps": [{"expr_str": "11 ⊗ 8", "result": 17}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊛ b = 3*a + 2*b + 2
Compute step by step: 12 ⊛ 10
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 58 | 2 | {"operators": [{"symbol": "⊛", "template_idx": 0, "coeffs": [3, 2, 2]}], "expression_tree": {"type": "op", "symbol": "⊛", "left": {"type": "leaf", "value": 12}, "right": {"type": "leaf", "value": 10}}, "expected_steps": [{"expr_str": "12 ⊛ 10", "result": 58}]} |
Below are definitions of new mathematical operators.
Definitions:
a ⊕ b = 2*a + 2*b + 3
Compute step by step: 2 ⊕ 12
Show each intermediate computation on its own line in the format:
<operand> <operator> <operand> = <expansion> = <result>
Then write your final answer as: Answer: <number> | 31 | 2 | {"operators": [{"symbol": "⊕", "template_idx": 0, "coeffs": [2, 2, 3]}], "expression_tree": {"type": "op", "symbol": "⊕", "left": {"type": "leaf", "value": 2}, "right": {"type": "leaf", "value": 12}}, "expected_steps": [{"expr_str": "2 ⊕ 12", "result": 31}]} |
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