{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 1, "expected": [-1, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 14\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 14, "expected": [-14, -7, -2, -1, 1, 2, 7, 14]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 0★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 0, "b": 5, "expected": 25}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 0★1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 0, "b": 1, "expected": 1}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 1★2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 1, "b": 2, "expected": 3}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 1★4\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 1, "b": 4, "expected": 15}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -5★-2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -5, "b": -2, "expected": -21}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -3★-1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -3, "b": -1, "expected": -8}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -4★-1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -4, "b": -1, "expected": -15}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 3★6\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 3, "b": 6, "expected": 27}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 5, "expected": [-5, -1, 1, 5]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 1, "expected": [-1, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 13\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 13, "expected": [-13, -1, 1, 13]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -4★-3\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -4, "b": -3, "expected": -7}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer a such that a★b = 11\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "a", "result": 11, "expected": [-11, -1, 1, 11]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -2★2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -2, "b": 2, "expected": 0}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -4★2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -4, "b": 2, "expected": -12}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer a such that a★b = 7\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "a", "result": 7, "expected": [-7, -1, 1, 7]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -4★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -4, "b": 5, "expected": 9}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 2, "expected": [-2, -1, 1, 2]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 12\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 12, "expected": [-12, -6, -4, -3, -2, -1, 1, 2, 3, 4, 6, 12]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -3★0\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -3, "b": 0, "expected": -9}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 1★2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 1, "b": 2, "expected": 3}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 2★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 2, "b": 5, "expected": 21}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer a such that a★b = 18\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "a", "result": 18, "expected": [-18, -9, -6, -3, -2, -1, 1, 2, 3, 6, 9, 18]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer a such that a★b = 17\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "a", "result": 17, "expected": [-17, -1, 1, 17]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer a such that a★b = 14\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "a", "result": 14, "expected": [-14, -7, -2, -1, 1, 2, 7, 14]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer a such that a★b = 7\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "a", "result": 7, "expected": [-7, -1, 1, 7]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 7★8\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 7, "b": 8, "expected": 15}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 4★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 4, "b": 5, "expected": 9}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer a such that a★b = 17\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "a", "result": 17, "expected": [-17, -1, 1, 17]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 3★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 3, "b": 5, "expected": 16}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -4★-3\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -4, "b": -3, "expected": -7}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 0★1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 0, "b": 1, "expected": 1}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 4★10\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 4, "b": 10, "expected": 84}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 4★7\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 4, "b": 7, "expected": 33}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer a such that a★b = 18\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "a", "result": 18, "expected": [-18, -9, -6, -3, -2, -1, 1, 2, 3, 6, 9, 18]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 4★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 4, "b": 5, "expected": 9}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 4★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 4, "b": 5, "expected": 9}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 0★1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 0, "b": 1, "expected": 1}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -2★2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -2, "b": 2, "expected": 0}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -3★-1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -3, "b": -1, "expected": -8}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 8\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 8, "expected": [-8, -4, -2, -1, 1, 2, 4, 8]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 0★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 0, "b": 5, "expected": 25}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 0★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 0, "b": 5, "expected": 25}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -3★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -3, "b": 5, "expected": 16}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 20\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 20, "expected": [-20, -10, -5, -4, -2, -1, 1, 2, 4, 5, 10, 20]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 1★5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 1, "b": 5, "expected": 24}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nFind integer b such that a★b = 7\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type1", "solve_var": "b", "result": 7, "expected": [-7, -1, 1, 7]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute -3★4\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": -3, "b": 4, "expected": 7}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nSolve 0★b = b\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "equation_type2", "expected": [0, 1]}}
{"data_source": "KorOperationUnicode2605", "prompt": "The operation a★b is defined as the definite integral of 2x from a to b.\nMathematically: a★b = ∫ₐᵇ 2x dx = b² - a².\n\nCompute 0★1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple answers use [[1or-2]] format.", "ground_truth": {"type": "compute", "a": 0, "b": 1, "expected": 1}}