{"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.\n\nFind integer pair such that a★b = 11\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 11, "expected": [[5, -6], [-5, -6], [-5, 6], [5, 6]]}}
{"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.\n\nCompute -3298★-1330\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -3298, "b": -1330, "expected": -9107904}}
{"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.\n\nFind integer pair such that a★b = 11\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 11, "expected": [[5, -6], [-5, -6], [-5, 6], [5, 6]]}}
{"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.\n\nFind integer pair such that a★b = 1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 1, "expected": [[0, -1], [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.\n\nCompute -443★-434\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -443, "b": -434, "expected": -7893}}
{"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.\n\nCompute -25★-24\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -25, "b": -24, "expected": -49}}
{"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.\n\nFind integer pair such that a★b = 4\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 4, "expected": [[0, -2], [0, 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.\n\nFind integer pair such that a★b = 16\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 16, "expected": [[3, -5], [-3, -5], [0, -4], [0, 4], [-3, 5], [3, 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.\n\nCompute 464★487\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 464, "b": 487, "expected": 21873}}
{"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.\n\nCompute 1665★3419\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 1665, "b": 3419, "expected": 8917336}}
{"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.\n\nCompute 13★25\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 13, "b": 25, "expected": 456}}
{"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.\n\nFind integer pair such that a★b = 12\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 12, "expected": [[2, -4], [-2, -4], [2, 4], [-2, 4]]}}
{"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.\n\nFind integer pair such that a★b = 2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 2, "expected": []}}
{"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.\n\nFind integer pair such that a★b = 15\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 15, "expected": [[7, -8], [-7, -8], [1, -4], [-1, -4], [-1, 4], [1, 4], [-7, 8], [7, 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.\n\nFind integer pair such that a★b = 5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 5, "expected": [[-2, -3], [2, -3], [2, 3], [-2, 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.\n\nFind integer pair such that a★b = 9\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 9, "expected": [[4, -5], [-4, -5], [0, -3], [0, 3], [4, 5], [-4, 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.\n\nFind integer pair such that a★b = 3\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 3, "expected": [[1, -2], [-1, -2], [1, 2], [-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.\n\nCompute 7★31\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 7, "b": 31, "expected": 912}}
{"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.\n\nCompute -39★-1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -39, "b": -1, "expected": -1520}}
{"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.\n\nCompute 130★277\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 130, "b": 277, "expected": 59829}}
{"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.\n\nCompute -227★-109\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -227, "b": -109, "expected": -39648}}
{"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.\n\nCompute 30★346\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 30, "b": 346, "expected": 118816}}
{"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.\n\nCompute 32★34\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 32, "b": 34, "expected": 132}}
{"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.\n\nFind integer pair such that a★b = 11\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 11, "expected": [[5, -6], [-5, -6], [-5, 6], [5, 6]]}}
{"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.\n\nFind integer pair such that a★b = 1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 1, "expected": [[0, -1], [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.\n\nCompute -31★23\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -31, "b": 23, "expected": -432}}
{"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.\n\nCompute -4★172\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -4, "b": 172, "expected": 29568}}
{"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.\n\nCompute 327★343\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 327, "b": 343, "expected": 10720}}
{"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.\n\nFind integer pair such that a★b = 18\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 18, "expected": []}}
{"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.\n\nFind integer pair such that a★b = 2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 2, "expected": []}}
{"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.\n\nFind integer pair such that a★b = 19\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 19, "expected": [[9, -10], [-9, -10], [9, 10], [-9, 10]]}}
{"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.\n\nFind integer pair such that a★b = 7\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 7, "expected": [[3, -4], [-3, -4], [-3, 4], [3, 4]]}}
{"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.\n\nCompute -372★-110\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -372, "b": -110, "expected": -126284}}
{"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.\n\nCompute 49★50\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 49, "b": 50, "expected": 99}}
{"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.\n\nFind integer pair such that a★b = 14\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 14, "expected": []}}
{"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.\n\nFind integer pair such that a★b = 12\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 12, "expected": [[2, -4], [-2, -4], [2, 4], [-2, 4]]}}
{"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.\n\nFind integer pair such that a★b = 11\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 11, "expected": [[5, -6], [-5, -6], [-5, 6], [5, 6]]}}
{"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.\n\nFind integer pair such that a★b = 16\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 16, "expected": [[3, -5], [-3, -5], [0, -4], [0, 4], [-3, 5], [3, 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.\n\nCompute 3360★4190\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 3360, "b": 4190, "expected": 6266500}}
{"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.\n\nCompute 426★483\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 426, "b": 483, "expected": 51813}}
{"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.\n\nCompute 187★270\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 187, "b": 270, "expected": 37931}}
{"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.\n\nFind integer pair such that a★b = 2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 2, "expected": []}}
{"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.\n\nFind integer pair such that a★b = 17\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 17, "expected": [[8, -9], [-8, -9], [8, 9], [-8, 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.\n\nCompute 151★3739\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 151, "b": 3739, "expected": 13957320}}
{"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.\n\nCompute 1442★2039\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 1442, "b": 2039, "expected": 2078157}}
{"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.\n\nCompute 1699★1949\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 1699, "b": 1949, "expected": 912000}}
{"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.\n\nCompute -2180★-19\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -2180, "b": -19, "expected": -4752039}}
{"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.\n\nFind integer pair such that a★b = 16\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 16, "expected": [[3, -5], [-3, -5], [0, -4], [0, 4], [-3, 5], [3, 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.\n\nCompute 0★16\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 0, "b": 16, "expected": 256}}
{"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.\n\nFind integer pair such that a★b = 11\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 11, "expected": [[5, -6], [-5, -6], [-5, 6], [5, 6]]}}
{"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.\n\nCompute -172★103\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -172, "b": 103, "expected": -18975}}
{"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.\n\nCompute -299★3239\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -299, "b": 3239, "expected": 10401720}}
{"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.\n\nCompute 303★390\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 303, "b": 390, "expected": 60291}}
{"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.\n\nFind integer pair such that a★b = 13\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 13, "expected": [[-6, -7], [6, -7], [6, 7], [-6, 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.\n\nCompute -2656★-1983\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -2656, "b": -1983, "expected": -3122047}}
{"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.\n\nFind integer pair such that a★b = 20\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 20, "expected": [[-4, -6], [4, -6], [4, 6], [-4, 6]]}}
{"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.\n\nFind integer pair such that a★b = 19\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 19, "expected": [[9, -10], [-9, -10], [9, 10], [-9, 10]]}}
{"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.\n\nCompute -1802★1462\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -1802, "b": 1462, "expected": -1109760}}
{"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.\n\nFind integer pair such that a★b = 2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 2, "expected": []}}
{"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.\n\nCompute -267★179\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -267, "b": 179, "expected": -39248}}
{"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.\n\nFind integer pair such that a★b = 18\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 18, "expected": []}}
{"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.\n\nCompute 43★46\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 43, "b": 46, "expected": 267}}
{"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.\n\nFind integer pair such that a★b = 20\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 20, "expected": [[-4, -6], [4, -6], [4, 6], [-4, 6]]}}
{"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.\n\nCompute 191★290\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 191, "b": 290, "expected": 47619}}
{"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.\n\nFind integer pair such that a★b = 9\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 9, "expected": [[4, -5], [-4, -5], [0, -3], [0, 3], [4, 5], [-4, 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.\n\nCompute -34★-26\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -34, "b": -26, "expected": -480}}
{"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.\n\nFind integer pair such that a★b = 3\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 3, "expected": [[1, -2], [-1, -2], [1, 2], [-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.\n\nFind integer pair such that a★b = 18\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 18, "expected": []}}
{"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.\n\nCompute -445★39\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -445, "b": 39, "expected": -196504}}
{"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.\n\nFind integer pair such that a★b = 1\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 1, "expected": [[0, -1], [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.\n\nCompute -1★40\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -1, "b": 40, "expected": 1599}}
{"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.\n\nFind integer pair such that a★b = 13\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 13, "expected": [[-6, -7], [6, -7], [6, 7], [-6, 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.\n\nFind integer pair such that a★b = 17\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 17, "expected": [[8, -9], [-8, -9], [8, 9], [-8, 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.\n\nCompute -1484★-761\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -1484, "b": -761, "expected": -1623135}}
{"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.\n\nCompute -9★-2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -9, "b": -2, "expected": -77}}
{"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.\n\nFind integer pair such that a★b = 15\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 15, "expected": [[7, -8], [-7, -8], [1, -4], [-1, -4], [-1, 4], [1, 4], [-7, 8], [7, 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.\n\nCompute -98★158\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -98, "b": 158, "expected": 15360}}
{"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.\n\nFind integer pair such that a★b = 16\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 16, "expected": [[3, -5], [-3, -5], [0, -4], [0, 4], [-3, 5], [3, 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.\n\nFind integer pair such that a★b = 5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 5, "expected": [[-2, -3], [2, -3], [2, 3], [-2, 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.\n\nFind integer pair such that a★b = 13\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 13, "expected": [[-6, -7], [6, -7], [6, 7], [-6, 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.\n\nCompute 356★391\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 356, "b": 391, "expected": 26145}}
{"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.\n\nCompute -225★275\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -225, "b": 275, "expected": 25000}}
{"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.\n\nCompute -1799★-861\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -1799, "b": -861, "expected": -2495080}}
{"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.\n\nFind integer pair such that a★b = 7\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 7, "expected": [[3, -4], [-3, -4], [-3, 4], [3, 4]]}}
{"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.\n\nCompute -2★45\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -2, "b": 45, "expected": 2021}}
{"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.\n\nFind integer pair such that a★b = 15\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 15, "expected": [[7, -8], [-7, -8], [1, -4], [-1, -4], [-1, 4], [1, 4], [-7, 8], [7, 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.\n\nCompute -286★693\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -286, "b": 693, "expected": 398453}}
{"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.\n\nFind integer pair such that a★b = 13\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 13, "expected": [[-6, -7], [6, -7], [6, 7], [-6, 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.\n\nCompute 468★495\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 468, "b": 495, "expected": 26001}}
{"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.\n\nFind integer pair such that a★b = 10\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 10, "expected": []}}
{"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.\n\nFind integer pair such that a★b = 12\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 12, "expected": [[2, -4], [-2, -4], [2, 4], [-2, 4]]}}
{"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.\n\nCompute -2796★3444\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -2796, "b": 3444, "expected": 4043520}}
{"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.\n\nCompute -21★13\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -21, "b": 13, "expected": -272}}
{"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.\n\nCompute 42★47\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 42, "b": 47, "expected": 445}}
{"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.\n\nFind integer pair such that a★b = 12\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 12, "expected": [[2, -4], [-2, -4], [2, 4], [-2, 4]]}}
{"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.\n\nFind integer pair such that a★b = 2\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 2, "expected": []}}
{"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.\n\nFind integer pair such that a★b = 5\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "equation_type1", "result": 5, "expected": [[-2, -3], [2, -3], [2, 3], [-2, 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.\n\nCompute 3929★4221\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 3929, "b": 4221, "expected": 2379800}}
{"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.\n\nCompute -17★-11\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": -17, "b": -11, "expected": -168}}
{"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.\n\nCompute 4198★4260\n\nPresent answer as integer(s) in [[ ]] brackets. For multiple pair answers use [[(a,b),(a,b),(a,b)]] format.", "ground_truth": {"type": "compute", "a": 4198, "b": 4260, "expected": 524396}}