{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②5 = 35, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 5, "c": 35}, "X": 1600}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 36.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 36}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①5)②2 = 20, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 5, "b": 2, "c": 20}, "X": 5625}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②2 = 8, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 2, "c": 8}, "X": 225}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (((16①9)①(144①4))②121).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "①", "left": {"operator": "①", "left": 16, "right": 9}, "right": {"operator": "①", "left": 144, "right": 4}}, "right": 121}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 9.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 9}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (9①(169①25)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 9, "right": {"operator": "①", "left": 169, "right": 25}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 4.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 4}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (64①(9②81)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 64, "right": {"operator": "②", "left": 9, "right": 81}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((49②4)②(9②4)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "②", "left": 49, "right": 4}, "right": {"operator": "②", "left": 9, "right": 4}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 16.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 16}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②1 = 2, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 1, "c": 2}, "X": 9}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((100①100)①(25②81)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": {"operator": "①", "left": 100, "right": 100}, "right": {"operator": "②", "left": 25, "right": 81}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②2 = 12, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 2, "c": 12}, "X": 1225}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②1 = 6, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 1, "c": 6}, "X": 729}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①6)②5 = 45, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 6, "b": 5, "c": 45}, "X": 2025}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 25.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 25}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①4)②4 = 20, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 4, "b": 4, "c": 20}, "X": 81}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 16.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 16}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (((1①4)①(9②4))②((169①36)②36)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "①", "left": {"operator": "①", "left": 1, "right": 4}, "right": {"operator": "②", "left": 9, "right": 4}}, "right": {"operator": "②", "left": {"operator": "①", "left": 169, "right": 36}, "right": 36}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②1 = 3, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 1, "c": 3}, "X": 64}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (16②(49①100)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": 16, "right": {"operator": "①", "left": 49, "right": 100}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((196①9)①(100①(49①121))).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": {"operator": "①", "left": 196, "right": 9}, "right": {"operator": "①", "left": 100, "right": {"operator": "①", "left": 49, "right": 121}}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②3 = 9, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 3, "c": 9}, "X": 64}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②4 = 32, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 4, "c": 32}, "X": 3025}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((225②25)②(9②9)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "②", "left": 225, "right": 25}, "right": {"operator": "②", "left": 9, "right": 9}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 400.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 400}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((25①16)②16).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "①", "left": 25, "right": 16}, "right": 16}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((4②25)②81).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "②", "left": 4, "right": 25}, "right": 81}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②2 = 6, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 2, "c": 6}, "X": 25}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (25①9).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 25, "right": 9}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (1①((25②4)②(9②100))).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 1, "right": {"operator": "②", "left": {"operator": "②", "left": 25, "right": 4}, "right": {"operator": "②", "left": 9, "right": 100}}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 4.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 4}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②5 = 15, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 5, "c": 15}, "X": 25}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②3 = 18, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 3, "c": 18}, "X": 1024}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((64①(25①16))①((36①81)②9)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": {"operator": "①", "left": 64, "right": {"operator": "①", "left": 25, "right": 16}}, "right": {"operator": "②", "left": {"operator": "①", "left": 36, "right": 81}, "right": 9}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((1②16)②(16①49)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "②", "left": 1, "right": 16}, "right": {"operator": "①", "left": 16, "right": 49}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 36.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 36}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②4 = 28, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 4, "c": 28}, "X": 1600}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①4)②2 = 14, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 4, "b": 2, "c": 14}, "X": 1089}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②4 = 32, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 4, "c": 32}, "X": 3025}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①4)②2 = 12, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 4, "b": 2, "c": 12}, "X": 400}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (64①144).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 64, "right": 144}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①6)②3 = 27, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 6, "b": 3, "c": 27}, "X": 2025}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((64②(9②36))②((9②144)②(225①324))).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "②", "left": 64, "right": {"operator": "②", "left": 9, "right": 36}}, "right": {"operator": "②", "left": {"operator": "②", "left": 9, "right": 144}, "right": {"operator": "①", "left": 225, "right": 324}}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((25②(144①289))①((121①121)②49)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": {"operator": "②", "left": 25, "right": {"operator": "①", "left": 144, "right": 289}}, "right": {"operator": "②", "left": {"operator": "①", "left": 121, "right": 121}, "right": 49}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②3 = 9, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 3, "c": 9}, "X": 64}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②3 = 12, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 3, "c": 12}, "X": 49}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②4 = 24, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 4, "c": 24}, "X": 1225}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 196.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 196}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②2 = 14, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 2, "c": 14}, "X": 1600}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①4)②3 = 24, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 4, "b": 3, "c": 24}, "X": 2304}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②5 = 30, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 5, "c": 30}, "X": 1024}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①4)②1 = 5, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 4, "b": 1, "c": 5}, "X": 81}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②1 = 2, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 1, "c": 2}, "X": 9}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 36.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 36}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②3 = 15, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 3, "c": 15}, "X": 256}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 16.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 16}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②3 = 9, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 3, "c": 9}, "X": 25}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (121①25).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 121, "right": 25}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 16.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 16}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (((9①144)①(1①36))②((49②144)②(169②196))).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "①", "left": {"operator": "①", "left": 9, "right": 144}, "right": {"operator": "①", "left": 1, "right": 36}}, "right": {"operator": "②", "left": {"operator": "②", "left": 49, "right": 144}, "right": {"operator": "②", "left": 169, "right": 196}}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②3 = 24, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 3, "c": 24}, "X": 3025}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②3 = 15, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 3, "c": 15}, "X": 256}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (64②(1①100)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": 64, "right": {"operator": "①", "left": 1, "right": 100}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 1.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 1}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((36②9)①16).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": {"operator": "②", "left": 36, "right": 9}, "right": 16}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①5)②1 = 9, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 5, "b": 1, "c": 9}, "X": 3136}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (36①49).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 36, "right": 49}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 100.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 100}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 36.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 36}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②3 = 21, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 3, "c": 21}, "X": 2025}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②1 = 6, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 1, "c": 6}, "X": 729}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②1 = 4, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 1, "c": 4}, "X": 144}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②6 = 18, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 6, "c": 18}, "X": 64}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①5)②2 = 14, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 5, "b": 2, "c": 14}, "X": 576}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②3 = 21, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 3, "c": 21}, "X": 1600}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 36.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 36}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①4)②4 = 36, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 4, "b": 4, "c": 36}, "X": 4225}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①4)②4 = 20, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 4, "b": 4, "c": 20}, "X": 81}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (1①169).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 1, "right": 169}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (1②100).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": 1, "right": 100}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 64.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 64}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②2 = 6, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 2, "c": 6}, "X": 25}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 361.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 361}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②2 = 14, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 2, "c": 14}, "X": 1600}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①2)②5 = 35, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 2, "b": 5, "c": 35}, "X": 2025}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②5 = 20, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 5, "c": 20}, "X": 49}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②4 = 20, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 4, "c": 20}, "X": 256}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute ((64②4)②49).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "②", "left": {"operator": "②", "left": 64, "right": 4}, "right": 49}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 1.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 1}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (((64②36)①(16②64))①64).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": {"operator": "①", "left": {"operator": "②", "left": 64, "right": 36}, "right": {"operator": "②", "left": 16, "right": 64}}, "right": 64}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute (9①(121①100)).\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": {"operator": "①", "left": 9, "right": {"operator": "①", "left": 121, "right": 100}}}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 16.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 16}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 4.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 4}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①1)②1 = 5, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 1, "b": 1, "c": 5}, "X": 576}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 49.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 49}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②3 = 24, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 3, "c": 24}, "X": 3025}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nCompute 81.\nPlease provide your answer in LaTeX format. Use \\frac{a}{b} for fractions and \\sqrt{x} for roots. Put your final answer within [[ ]].", "ground_truth": {"type": "compute", "expression": 81}}
{"data_source": "KorOperationUnicode0033", "prompt": "a①b=\\sqrt{a}+b^2.\na②b=\\sqrt{a}×b.\nIf (X①3)②6 = 24, find X.\nProvide only a numeric answer within [[ ]].", "ground_truth": {"type": "solve", "equation": {"a": 3, "b": 6, "c": 24}, "X": 49}}