Datasets:

danyarm
/

ckg-benchmark

+{"id": "calculus_T1_328", "domain": "calculus", "type": "T1_entity", "query": "What is Integral of a to x?", "ground_truth": ["Integral of a to x", "INTEG"], "concept_id": 328, "hop_depth": 0}
+{"id": "calculus_T1_58", "domain": "calculus", "type": "T1_entity", "query": "What is Removable Discontinuity?", "ground_truth": ["Removable Discontinuity", "CONT"], "concept_id": 58, "hop_depth": 0}
+{"id": "calculus_T1_13", "domain": "calculus", "type": "T1_entity", "query": "What is Logarithmic Function?", "ground_truth": ["Logarithmic Function", "FOUND"], "concept_id": 13, "hop_depth": 0}
+{"id": "calculus_T1_380", "domain": "calculus", "type": "T1_entity", "query": "What is Integration Strategy?", "ground_truth": ["Integration Strategy", "TECH"], "concept_id": 380, "hop_depth": 0}
+{"id": "calculus_T1_141", "domain": "calculus", "type": "T1_entity", "query": "What is Derivative of log x?", "ground_truth": ["Derivative of log x", "DRULE"], "concept_id": 141, "hop_depth": 0}
+{"id": "calculus_T1_126", "domain": "calculus", "type": "T1_entity", "query": "What is Derivative of Root?", "ground_truth": ["Derivative of Root", "DRULE"], "concept_id": 126, "hop_depth": 0}
+{"id": "calculus_T1_115", "domain": "calculus", "type": "T1_entity", "query": "What is Derivative Rules?", "ground_truth": ["Derivative Rules", "DRULE"], "concept_id": 115, "hop_depth": 0}
+{"id": "calculus_T1_72", "domain": "calculus", "type": "T1_entity", "query": "What is Vertical Asymptote?", "ground_truth": ["Vertical Asymptote", "ASYM"], "concept_id": 72, "hop_depth": 0}
+{"id": "calculus_T1_378", "domain": "calculus", "type": "T1_entity", "query": "What is Completing Square?", "ground_truth": ["Completing Square", "TECH"], "concept_id": 378, "hop_depth": 0}
+{"id": "calculus_T1_53", "domain": "calculus", "type": "T1_entity", "query": "What is Three Conditions?", "ground_truth": ["Three Conditions", "CONT"], "concept_id": 53, "hop_depth": 0}
+{"id": "calculus_T1_347", "domain": "calculus", "type": "T1_entity", "query": "What is Fundamental Theorem?", "ground_truth": ["Fundamental Theorem", "FTC"], "concept_id": 347, "hop_depth": 0}
+{"id": "calculus_T1_280", "domain": "calculus", "type": "T1_entity", "query": "What is Symmetry Analysis?", "ground_truth": ["Symmetry Analysis", "CURV"], "concept_id": 280, "hop_depth": 0}
+{"id": "calculus_T1_45", "domain": "calculus", "type": "T1_entity", "query": "What is Sin x Over x Limit?", "ground_truth": ["Sin x Over x Limit", "LIMIT"], "concept_id": 45, "hop_depth": 0}
+{"id": "calculus_T1_303", "domain": "calculus", "type": "T1_entity", "query": "What is Verifying Minimum?", "ground_truth": ["Verifying Minimum", "OPT"], "concept_id": 303, "hop_depth": 0}
+{"id": "calculus_T1_217", "domain": "calculus", "type": "T1_entity", "query": "What is Marginal Analysis?", "ground_truth": ["Marginal Analysis", "APPL"], "concept_id": 217, "hop_depth": 0}
+{"id": "calculus_T1_17", "domain": "calculus", "type": "T1_entity", "query": "What is Trigonometric Identities?", "ground_truth": ["Trigonometric Identities", "FOUND"], "concept_id": 17, "hop_depth": 0}
+{"id": "calculus_T1_16", "domain": "calculus", "type": "T1_entity", "query": "What is Radian Measure?", "ground_truth": ["Radian Measure", "FOUND"], "concept_id": 16, "hop_depth": 0}
+{"id": "calculus_T1_48", "domain": "calculus", "type": "T1_entity", "query": "What is Limits from Tables?", "ground_truth": ["Limits from Tables", "LIMIT"], "concept_id": 48, "hop_depth": 0}
+{"id": "calculus_T1_112", "domain": "calculus", "type": "T1_entity", "query": "What is Local Linearity?", "ground_truth": ["Local Linearity", "DERIV"], "concept_id": 112, "hop_depth": 0}
+{"id": "calculus_T1_120", "domain": "calculus", "type": "T1_entity", "query": "What is Constant Multiple Deriv?", "ground_truth": ["Constant Multiple Deriv", "DRULE"], "concept_id": 120, "hop_depth": 0}
+{"id": "calculus_T1_259", "domain": "calculus", "type": "T1_entity", "query": "What is Increasing Function?", "ground_truth": ["Increasing Function", "ANAL"], "concept_id": 259, "hop_depth": 0}
+{"id": "calculus_T1_309", "domain": "calculus", "type": "T1_entity", "query": "What is Integral Notation?", "ground_truth": ["Integral Notation", "INTEG"], "concept_id": 309, "hop_depth": 0}
+{"id": "calculus_T1_14", "domain": "calculus", "type": "T1_entity", "query": "What is Trigonometric Function?", "ground_truth": ["Trigonometric Function", "FOUND"], "concept_id": 14, "hop_depth": 0}
+{"id": "calculus_T1_288", "domain": "calculus", "type": "T1_entity", "query": "What is Objective Function?", "ground_truth": ["Objective Function", "OPT"], "concept_id": 288, "hop_depth": 0}
+{"id": "calculus_T1_102", "domain": "calculus", "type": "T1_entity", "query": "What is One-Sided Derivative?", "ground_truth": ["One-Sided Derivative", "DERIV"], "concept_id": 102, "hop_depth": 0}
+{"id": "calculus_T1_367", "domain": "calculus", "type": "T1_entity", "query": "What is Average Value?", "ground_truth": ["Average Value", "FTC"], "concept_id": 367, "hop_depth": 0}
+{"id": "calculus_T1_333", "domain": "calculus", "type": "T1_entity", "query": "What is Arctan Integral?", "ground_truth": ["Arctan Integral", "INTEG"], "concept_id": 333, "hop_depth": 0}
+{"id": "calculus_T1_360", "domain": "calculus", "type": "T1_entity", "query": "What is Reversing Limits?", "ground_truth": ["Reversing Limits", "FTC"], "concept_id": 360, "hop_depth": 0}
+{"id": "calculus_T1_215", "domain": "calculus", "type": "T1_entity", "query": "What is dx Notation?", "ground_truth": ["dx Notation", "APPL"], "concept_id": 215, "hop_depth": 0}
+{"id": "calculus_T1_113", "domain": "calculus", "type": "T1_entity", "query": "What is Tangent Approximation?", "ground_truth": ["Tangent Approximation", "DERIV"], "concept_id": 113, "hop_depth": 0}
+{"id": "calculus_T1_230", "domain": "calculus", "type": "T1_entity", "query": "What is Zero Over Zero Apply?", "ground_truth": ["Zero Over Zero Apply", "APPL"], "concept_id": 230, "hop_depth": 0}
+{"id": "calculus_T1_302", "domain": "calculus", "type": "T1_entity", "query": "What is Verifying Maximum?", "ground_truth": ["Verifying Maximum", "OPT"], "concept_id": 302, "hop_depth": 0}
+{"id": "calculus_T1_143", "domain": "calculus", "type": "T1_entity", "query": "What is Simplifying First?", "ground_truth": ["Simplifying First", "DRULE"], "concept_id": 143, "hop_depth": 0}
+{"id": "calculus_T1_4", "domain": "calculus", "type": "T1_entity", "query": "What is Composite Function?", "ground_truth": ["Composite Function", "FOUND"], "concept_id": 4, "hop_depth": 0}
+{"id": "calculus_T1_82", "domain": "calculus", "type": "T1_entity", "query": "What is Exponential Growth Rate?", "ground_truth": ["Exponential Growth Rate", "ASYM"], "concept_id": 82, "hop_depth": 0}
+{"id": "calculus_T1_358", "domain": "calculus", "type": "T1_entity", "query": "What is Integral Properties?", "ground_truth": ["Integral Properties", "FTC"], "concept_id": 358, "hop_depth": 0}
+{"id": "calculus_T1_175", "domain": "calculus", "type": "T1_entity", "query": "What is Derivative of Arctan?", "ground_truth": ["Derivative of Arctan", "IMPL"], "concept_id": 175, "hop_depth": 0}
+{"id": "calculus_T1_80", "domain": "calculus", "type": "T1_entity", "query": "What is Dominant Term?", "ground_truth": ["Dominant Term", "ASYM"], "concept_id": 80, "hop_depth": 0}
+{"id": "calculus_T1_111", "domain": "calculus", "type": "T1_entity", "query": "What is Continuous Not Implies?", "ground_truth": ["Continuous Not Implies", "DERIV"], "concept_id": 111, "hop_depth": 0}
+{"id": "calculus_T1_173", "domain": "calculus", "type": "T1_entity", "query": "What is Derivative of Arcsin?", "ground_truth": ["Derivative of Arcsin", "IMPL"], "concept_id": 173, "hop_depth": 0}
+{"id": "calculus_T1_195", "domain": "calculus", "type": "T1_entity", "query": "What is Speed vs Velocity?", "ground_truth": ["Speed vs Velocity", "HIGH"], "concept_id": 195, "hop_depth": 0}
+{"id": "calculus_T1_50", "domain": "calculus", "type": "T1_entity", "query": "What is Infinite Limit?", "ground_truth": ["Infinite Limit", "LIMIT"], "concept_id": 50, "hop_depth": 0}
+{"id": "calculus_T1_184", "domain": "calculus", "type": "T1_entity", "query": "What is Higher-Order Derivative?", "ground_truth": ["Higher-Order Derivative", "HIGH"], "concept_id": 184, "hop_depth": 0}
+{"id": "calculus_T1_177", "domain": "calculus", "type": "T1_entity", "query": "What is Derivative of Arccsc?", "ground_truth": ["Derivative of Arccsc", "IMPL"], "concept_id": 177, "hop_depth": 0}
+{"id": "calculus_T1_310", "domain": "calculus", "type": "T1_entity", "query": "What is Integrand?", "ground_truth": ["Integrand", "INTEG"], "concept_id": 310, "hop_depth": 0}
+{"id": "calculus_T1_136", "domain": "calculus", "type": "T1_entity", "query": "What is Derivative of Secant?", "ground_truth": ["Derivative of Secant", "DRULE"], "concept_id": 136, "hop_depth": 0}
+{"id": "calculus_T1_23", "domain": "calculus", "type": "T1_entity", "query": "What is Intuitive Limit?", "ground_truth": ["Intuitive Limit", "LIMIT"], "concept_id": 23, "hop_depth": 0}
+{"id": "calculus_T1_374", "domain": "calculus", "type": "T1_entity", "query": "What is Back Substitution?", "ground_truth": ["Back Substitution", "TECH"], "concept_id": 374, "hop_depth": 0}
+{"id": "calculus_T1_236", "domain": "calculus", "type": "T1_entity", "query": "What is Repeated L'Hospital?", "ground_truth": ["Repeated L'Hospital", "APPL"], "concept_id": 236, "hop_depth": 0}
+{"id": "calculus_T1_275", "domain": "calculus", "type": "T1_entity", "query": "What is Graph from Derivative?", "ground_truth": ["Graph from Derivative", "CURV"], "concept_id": 275, "hop_depth": 0}
+{"id": "calculus_T2_66", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Continuity of Polynomials?", "ground_truth": ["Polynomial Function", "Continuous Function"], "concept_id": 66, "hop_depth": 1}
+{"id": "calculus_T2_196", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Direction of Motion?", "ground_truth": ["Speed vs Velocity"], "concept_id": 196, "hop_depth": 1}
+{"id": "calculus_T2_43", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Squeeze Theorem?", "ground_truth": ["Limit Laws"], "concept_id": 43, "hop_depth": 1}
+{"id": "calculus_T2_285", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Inflection Analysis?", "ground_truth": ["Inflection Point", "Curve Sketching"], "concept_id": 285, "hop_depth": 1}
+{"id": "calculus_T2_153", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Power Chain Rule?", "ground_truth": ["Chain Rule Formula", "Power Rule Derivative"], "concept_id": 153, "hop_depth": 1}
+{"id": "calculus_T2_324", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Integral of Csc Squared?", "ground_truth": ["Basic Trig Integrals"], "concept_id": 324, "hop_depth": 1}
+{"id": "calculus_T2_319", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Constant Multiple Integ?", "ground_truth": ["Indefinite Integral"], "concept_id": 319, "hop_depth": 1}
+{"id": "calculus_T2_188", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Second Deriv Notation?", "ground_truth": ["Second Derivative"], "concept_id": 188, "hop_depth": 1}
+{"id": "calculus_T2_298", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Can Problem?", "ground_truth": ["Maximizing Volume"], "concept_id": 298, "hop_depth": 1}
+{"id": "calculus_T2_101", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Differentiability Point?", "ground_truth": ["Differentiability", "Derivative at a Point"], "concept_id": 101, "hop_depth": 1}
+{"id": "calculus_T2_363", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Integral Bounds Split?", "ground_truth": ["Additivity Property"], "concept_id": 363, "hop_depth": 1}
+{"id": "calculus_T2_38", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Infinity Over Infinity?", "ground_truth": ["Indeterminate Form"], "concept_id": 38, "hop_depth": 1}
+{"id": "calculus_T2_26", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Right-Hand Limit?", "ground_truth": ["One-Sided Limit"], "concept_id": 26, "hop_depth": 1}
+{"id": "calculus_T2_341", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Sigma Notation?", "ground_truth": ["Summation Notation"], "concept_id": 341, "hop_depth": 1}
+{"id": "calculus_T2_119", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Difference Rule Deriv?", "ground_truth": ["Derivative Rules"], "concept_id": 119, "hop_depth": 1}
+{"id": "calculus_T2_151", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Derivative of f of g?", "ground_truth": ["Composition Derivative"], "concept_id": 151, "hop_depth": 1}
+{"id": "calculus_T2_122", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Polynomial Derivative?", "ground_truth": ["Power Rule Derivative", "Linear Combination"], "concept_id": 122, "hop_depth": 1}
+{"id": "calculus_T2_54", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Continuity on Interval?", "ground_truth": ["Continuity at a Point"], "concept_id": 54, "hop_depth": 1}
+{"id": "calculus_T2_197", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Speeding Up Slowing?", "ground_truth": ["Acceleration", "Direction of Motion"], "concept_id": 197, "hop_depth": 1}
+{"id": "calculus_T2_145", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Chain Rule Formula?", "ground_truth": ["Chain Rule"], "concept_id": 145, "hop_depth": 1}
+{"id": "calculus_T2_235", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for One to Infinity?", "ground_truth": ["Indeterminate Powers"], "concept_id": 235, "hop_depth": 1}
+{"id": "calculus_T2_328", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Integral of a to x?", "ground_truth": ["Integral of e to x"], "concept_id": 328, "hop_depth": 1}
+{"id": "calculus_T2_189", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for f Double Prime?", "ground_truth": ["Second Deriv Notation"], "concept_id": 189, "hop_depth": 1}
+{"id": "calculus_T2_86", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Average Rate of Change?", "ground_truth": ["Rate of Change"], "concept_id": 86, "hop_depth": 1}
+{"id": "calculus_T2_192", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Acceleration?", "ground_truth": ["Velocity from Position"], "concept_id": 192, "hop_depth": 1}
+{"id": "calculus_T2_184", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Higher-Order Derivative?", "ground_truth": ["Derivative Function"], "concept_id": 184, "hop_depth": 1}
+{"id": "calculus_T2_110", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Diff Implies Continuous?", "ground_truth": ["Differentiability", "Continuous Function"], "concept_id": 110, "hop_depth": 1}
+{"id": "calculus_T2_346", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Limits of Integration?", "ground_truth": ["Definite Integral Notat"], "concept_id": 346, "hop_depth": 1}
+{"id": "calculus_T2_139", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Derivative of a to x?", "ground_truth": ["Derivative of e to x"], "concept_id": 139, "hop_depth": 1}
+{"id": "calculus_T2_362", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Integral of Sum?", "ground_truth": ["Integral Properties"], "concept_id": 362, "hop_depth": 1}
+{"id": "calculus_T2_352", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Integral as Function?", "ground_truth": ["Accumulation Function"], "concept_id": 352, "hop_depth": 1}
+{"id": "calculus_T2_334", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Arcsec Integral?", "ground_truth": ["Inverse Trig Integrals"], "concept_id": 334, "hop_depth": 1}
+{"id": "calculus_T2_39", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Algebraic Limit Technique?", "ground_truth": ["Indeterminate Form", "Zero Over Zero Form"], "concept_id": 39, "hop_depth": 1}
+{"id": "calculus_T2_314", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Particular Antideriv?", "ground_truth": ["General Antiderivative"], "concept_id": 314, "hop_depth": 1}
+{"id": "calculus_T2_90", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Tangent Line?", "ground_truth": ["Secant Line", "Limit"], "concept_id": 90, "hop_depth": 1}
+{"id": "calculus_T2_276", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Derivative from Graph?", "ground_truth": ["Graph from Derivative"], "concept_id": 276, "hop_depth": 1}
+{"id": "calculus_T2_376", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Changing Bounds?", "ground_truth": ["Definite Substitution"], "concept_id": 376, "hop_depth": 1}
+{"id": "calculus_T2_128", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Product Rule Formula?", "ground_truth": ["Product Rule"], "concept_id": 128, "hop_depth": 1}
+{"id": "calculus_T2_239", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for MVT Statement?", "ground_truth": ["Mean Value Theorem"], "concept_id": 239, "hop_depth": 1}
+{"id": "calculus_T2_141", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Derivative of log x?", "ground_truth": ["Derivative of ln x"], "concept_id": 141, "hop_depth": 1}
+{"id": "calculus_T2_330", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Natural Log Integral?", "ground_truth": ["Integral of 1 Over x"], "concept_id": 330, "hop_depth": 1}
+{"id": "calculus_T2_355", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Net Change Theorem?", "ground_truth": ["FTC Part Two"], "concept_id": 355, "hop_depth": 1}
+{"id": "calculus_T2_288", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Objective Function?", "ground_truth": ["Optimization Problem"], "concept_id": 288, "hop_depth": 1}
+{"id": "calculus_T2_115", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Derivative Rules?", "ground_truth": ["Derivative Function"], "concept_id": 115, "hop_depth": 1}
+{"id": "calculus_T2_353", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Derivative of Integral?", "ground_truth": ["FTC Part One"], "concept_id": 353, "hop_depth": 1}
+{"id": "calculus_T2_169", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Inverse Function Thm?", "ground_truth": ["Inverse Function", "Derivative Function"], "concept_id": 169, "hop_depth": 1}
+{"id": "calculus_T2_31", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Product Rule for Limits?", "ground_truth": ["Limit Laws"], "concept_id": 31, "hop_depth": 1}
+{"id": "calculus_T2_120", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Constant Multiple Deriv?", "ground_truth": ["Derivative Rules"], "concept_id": 120, "hop_depth": 1}
+{"id": "calculus_T2_19", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Number Line?", "ground_truth": ["Coordinate System"], "concept_id": 19, "hop_depth": 1}
+{"id": "calculus_T2_164", "domain": "calculus", "type": "T2_dependency", "query": "What are the prerequisites for Treating y as Function?", "ground_truth": ["Implicit Differentiation"], "concept_id": 164, "hop_depth": 1}
+{"id": "calculus_T3_1_139", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Derivative of a to x?", "ground_truth": ["Derivative of a to x", "Derivative of e to x", "Exponential Function", "Function"], "concept_id": 139, "hop_depth": 3, "path_ids": [139, 138, 12, 1]}
+{"id": "calculus_T3_18_102", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Coordinate System to One-Sided Derivative?", "ground_truth": ["One-Sided Derivative", "One-Sided Limit", "Limit", "Real Numbers", "Number Line", "Coordinate System"], "concept_id": 102, "hop_depth": 5, "path_ids": [102, 24, 21, 20, 19, 18]}
+{"id": "calculus_T3_1_322", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Integral of Cos x?", "ground_truth": ["Integral of Cos x", "Basic Trig Integrals", "Derivative of Sine", "Trigonometric Function", "Function"], "concept_id": 322, "hop_depth": 4, "path_ids": [322, 320, 132, 14, 1]}
+{"id": "calculus_T3_1_77", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Behavior Near Asymptote?", "ground_truth": ["Behavior Near Asymptote", "Limit at Infinity", "Limit", "Function"], "concept_id": 77, "hop_depth": 3, "path_ids": [77, 75, 21, 1]}
+{"id": "calculus_T3_1_372", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Choosing u?", "ground_truth": ["Choosing u", "Substitution Method", "u-Substitution", "Chain Rule", "Composite Function", "Function"], "concept_id": 372, "hop_depth": 5, "path_ids": [372, 371, 370, 144, 4, 1]}
+{"id": "calculus_T3_1_372", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Choosing u?", "ground_truth": ["Choosing u", "Substitution Method", "u-Substitution", "Chain Rule", "Composite Function", "Function"], "concept_id": 372, "hop_depth": 5, "path_ids": [372, 371, 370, 144, 4, 1]}
+{"id": "calculus_T3_1_372", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Choosing u?", "ground_truth": ["Choosing u", "Substitution Method", "u-Substitution", "Chain Rule", "Composite Function", "Function"], "concept_id": 372, "hop_depth": 5, "path_ids": [372, 371, 370, 144, 4, 1]}
+{"id": "calculus_T3_18_77", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Coordinate System to Behavior Near Asymptote?", "ground_truth": ["Behavior Near Asymptote", "Limit at Infinity", "Limit", "Real Numbers", "Number Line", "Coordinate System"], "concept_id": 77, "hop_depth": 5, "path_ids": [77, 75, 21, 20, 19, 18]}
+{"id": "calculus_T3_1_165", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Implicit Chain Rule?", "ground_truth": ["Implicit Chain Rule", "Chain Rule", "Composite Function", "Function"], "concept_id": 165, "hop_depth": 3, "path_ids": [165, 144, 4, 1]}
+{"id": "calculus_T3_1_106", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Vertical Tangent Point?", "ground_truth": ["Vertical Tangent Point", "Tangent Line", "Limit", "Function"], "concept_id": 106, "hop_depth": 3, "path_ids": [106, 90, 21, 1]}
+{"id": "calculus_T3_1_336", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Left Riemann Sum?", "ground_truth": ["Left Riemann Sum", "Riemann Sum", "Average Rate of Change", "Rate of Change", "Function"], "concept_id": 336, "hop_depth": 4, "path_ids": [336, 335, 86, 85, 1]}
+{"id": "calculus_T3_1_77", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Behavior Near Asymptote?", "ground_truth": ["Behavior Near Asymptote", "Limit at Infinity", "Limit", "Function"], "concept_id": 77, "hop_depth": 3, "path_ids": [77, 75, 21, 1]}
+{"id": "calculus_T3_1_49", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Numerical Estimation?", "ground_truth": ["Numerical Estimation", "Limits from Tables", "Intuitive Limit", "Limit", "Function"], "concept_id": 49, "hop_depth": 4, "path_ids": [49, 48, 23, 21, 1]}
+{"id": "calculus_T3_1_324", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Integral of Csc Squared?", "ground_truth": ["Integral of Csc Squared", "Basic Trig Integrals", "Derivative of Sine", "Trigonometric Function", "Function"], "concept_id": 324, "hop_depth": 4, "path_ids": [324, 320, 132, 14, 1]}
+{"id": "calculus_T3_1_65", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Continuity of Composites?", "ground_truth": ["Continuity of Composites", "Composite Function", "Function"], "concept_id": 65, "hop_depth": 2, "path_ids": [65, 4, 1]}
+{"id": "calculus_T3_18_59", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Coordinate System to Jump Discontinuity?", "ground_truth": ["Jump Discontinuity", "One-Sided Limit", "Limit", "Real Numbers", "Number Line", "Coordinate System"], "concept_id": 59, "hop_depth": 5, "path_ids": [59, 24, 21, 20, 19, 18]}
+{"id": "calculus_T3_1_82", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Exponential Growth Rate?", "ground_truth": ["Exponential Growth Rate", "Exponential Function", "Function"], "concept_id": 82, "hop_depth": 2, "path_ids": [82, 12, 1]}
+{"id": "calculus_T3_1_165", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Implicit Chain Rule?", "ground_truth": ["Implicit Chain Rule", "Chain Rule", "Composite Function", "Function"], "concept_id": 165, "hop_depth": 3, "path_ids": [165, 144, 4, 1]}
+{"id": "calculus_T3_1_150", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Leibniz Chain Rule?", "ground_truth": ["Leibniz Chain Rule", "Chain Rule Formula", "Chain Rule", "Composite Function", "Function"], "concept_id": 150, "hop_depth": 4, "path_ids": [150, 145, 144, 4, 1]}
+{"id": "calculus_T3_1_204", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Ladder Problem?", "ground_truth": ["Ladder Problem", "Related Rates", "Instantaneous Rate", "Limit", "Function"], "concept_id": 204, "hop_depth": 4, "path_ids": [204, 199, 87, 21, 1]}
+{"id": "calculus_T3_1_332", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Arcsin Integral?", "ground_truth": ["Arcsin Integral", "Inverse Trig Integrals", "Derivative of Arcsin", "Trigonometric Function", "Function"], "concept_id": 332, "hop_depth": 4, "path_ids": [332, 331, 173, 14, 1]}
+{"id": "calculus_T3_1_332", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Arcsin Integral?", "ground_truth": ["Arcsin Integral", "Inverse Trig Integrals", "Derivative of Arcsin", "Trigonometric Function", "Function"], "concept_id": 332, "hop_depth": 4, "path_ids": [332, 331, 173, 14, 1]}
+{"id": "calculus_T3_1_16", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Radian Measure?", "ground_truth": ["Radian Measure", "Unit Circle", "Trigonometric Function", "Function"], "concept_id": 16, "hop_depth": 3, "path_ids": [16, 15, 14, 1]}
+{"id": "calculus_T3_1_151", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Derivative of f of g?", "ground_truth": ["Derivative of f of g", "Composition Derivative", "Chain Rule", "Composite Function", "Function"], "concept_id": 151, "hop_depth": 4, "path_ids": [151, 146, 144, 4, 1]}
+{"id": "calculus_T3_1_40", "domain": "calculus", "type": "T3_path", "query": "What is the prerequisite chain from Function to Factoring for Limits?", "ground_truth": ["Factoring for Limits", "Algebraic Limit Technique", "Indeterminate Form", "Direct Substitution", "Polynomial Function", "Function"], "concept_id": 40, "hop_depth": 5, "path_ids": [40, 39, 36, 35, 10, 1]}
+{"id": "calculus_T4_FOUND", "domain": "calculus", "type": "T4_aggregate", "query": "List all FOUND concepts in this knowledge graph", "ground_truth": ["Function", "Domain and Range", "Function Notation", "Composite Function", "Inverse Function", "Graphing Functions", "Piecewise Function", "Even and Odd Functions", "Function Transformations", "Polynomial Function", "Rational Function", "Exponential Function", "Logarithmic Function", "Trigonometric Function", "Unit Circle", "Radian Measure", "Trigonometric Identities", "Coordinate System", "Number Line", "Real Numbers"], "taxonomy_id": "FOUND", "hop_depth": 0}
+{"id": "calculus_T4_LIMIT", "domain": "calculus", "type": "T4_aggregate", "query": "List all LIMIT concepts in this knowledge graph", "ground_truth": ["Limit", "Limit Notation", "Intuitive Limit", "One-Sided Limit", "Left-Hand Limit", "Right-Hand Limit", "Two-Sided Limit", "Limit Existence", "Limit Laws", "Sum Rule for Limits", "Product Rule for Limits", "Quotient Rule for Limits", "Constant Multiple Rule", "Power Rule for Limits", "Direct Substitution", "Indeterminate Form", "Zero Over Zero Form", "Infinity Over Infinity", "Algebraic Limit Technique", "Factoring for Limits", "Rationalization", "Complex Fractions", "Squeeze Theorem", "Special Trig Limits", "Sin x Over x Limit", "Limit of Composition", "Limits from Graphs", "Limits from Tables", "Numerical Estimation", "Infinite Limit"], "taxonomy_id": "LIMIT", "hop_depth": 0}
+{"id": "calculus_T4_CONT", "domain": "calculus", "type": "T4_aggregate", "query": "List all CONT concepts in this knowledge graph", "ground_truth": ["Continuity", "Continuity at a Point", "Three Conditions", "Continuity on Interval", "One-Sided Continuity", "Continuous Function", "Discontinuity", "Removable Discontinuity", "Jump Discontinuity", "Infinite Discontinuity", "Essential Discontinuity", "Continuous Extension", "Removing Discontinuities", "Piecewise Continuity", "Continuity of Composites", "Continuity of Polynomials", "Continuity of Rationals", "Continuity of Trig", "Continuity of Exp Log", "Intermediate Value Thm"], "taxonomy_id": "CONT", "hop_depth": 0}
+{"id": "calculus_T4_ASYM", "domain": "calculus", "type": "T4_aggregate", "query": "List all ASYM concepts in this knowledge graph", "ground_truth": ["Asymptote", "Vertical Asymptote", "Horizontal Asymptote", "Oblique Asymptote", "Limit at Infinity", "End Behavior", "Behavior Near Asymptote", "One-Sided Infinite Limit", "Comparing Growth Rates", "Dominant Term", "Rational End Behavior", "Exponential Growth Rate", "Logarithmic Growth Rate", "Polynomial Growth Rate"], "taxonomy_id": "ASYM", "hop_depth": 0}
+{"id": "calculus_T4_DERIV", "domain": "calculus", "type": "T4_aggregate", "query": "List all DERIV concepts in this knowledge graph", "ground_truth": ["Rate of Change", "Average Rate of Change", "Instantaneous Rate", "Difference Quotient", "Secant Line", "Tangent Line", "Slope of Tangent", "Derivative Definition", "Limit Definition Deriv", "Derivative at a Point", "Derivative Function", "Derivative Notation", "Prime Notation", "Leibniz Notation", "Differentiable Function", "Differentiability", "Differentiability Point", "One-Sided Derivative", "Non-Differentiable Pts", "Corner Point", "Cusp", "Vertical Tangent Point", "Derivative from Graph", "Derivative from Table", "Symmetric Difference", "Diff Implies Continuous", "Continuous Not Implies", "Local Linearity", "Tangent Approximation", "Instantaneous Velocity"], "taxonomy_id": "DERIV", "hop_depth": 0}
+{"id": "calculus_T4_DRULE", "domain": "calculus", "type": "T4_aggregate", "query": "List all DRULE concepts in this knowledge graph", "ground_truth": ["Derivative Rules", "Constant Rule", "Power Rule Derivative", "Sum Rule Derivative", "Difference Rule Deriv", "Constant Multiple Deriv", "Linear Combination", "Polynomial Derivative", "Derivative of x to n", "Negative Exponent Deriv", "Fractional Exponent", "Derivative of Root", "Product Rule", "Product Rule Formula", "Quotient Rule", "Quotient Rule Formula", "Reciprocal Rule", "Derivative of Sine", "Derivative of Cosine", "Derivative of Tangent", "Derivative of Cotangent", "Derivative of Secant", "Derivative of Cosecant", "Derivative of e to x", "Derivative of a to x", "Derivative of ln x", "Derivative of log x", "Combining Rules", "Simplifying First"], "taxonomy_id": "DRULE", "hop_depth": 0}
+{"id": "calculus_T4_CHAIN", "domain": "calculus", "type": "T4_aggregate", "query": "List all CHAIN concepts in this knowledge graph", "ground_truth": ["Chain Rule", "Chain Rule Formula", "Composition Derivative", "Inside Function", "Outside Function", "Nested Chain Rule", "Leibniz Chain Rule", "Derivative of f of g", "Recognizing Composition", "Power Chain Rule", "Trig Chain Rule", "Exponential Chain Rule", "Log Chain Rule", "Multiple Chain Rule", "General Power Rule", "Combining Chain Rule"], "taxonomy_id": "CHAIN", "hop_depth": 0}
+{"id": "calculus_T4_IMPL", "domain": "calculus", "type": "T4_aggregate", "query": "List all IMPL concepts in this knowledge graph", "ground_truth": ["Implicit Function", "Implicit Equation", "Implicit Differentiation", "dy dx Implicitly", "Treating y as Function", "Implicit Chain Rule", "Solving for dy dx", "Second Deriv Implicit", "Tangent Line Implicit", "Inverse Function Thm", "Derivative of Inverse", "Inverse Deriv Formula", "Graphical Inverse Deriv", "Derivative of Arcsin", "Derivative of Arccos", "Derivative of Arctan", "Derivative of Arcsec", "Derivative of Arccsc", "Derivative of Arccot", "Inverse Trig Domain", "Logarithmic Differentiate", "Differentiating Products", "Differentiating Powers", "Variable Exponents"], "taxonomy_id": "IMPL", "hop_depth": 0}
+{"id": "calculus_T4_HIGH", "domain": "calculus", "type": "T4_aggregate", "query": "List all HIGH concepts in this knowledge graph", "ground_truth": ["Higher-Order Derivative", "Second Derivative", "Third Derivative", "nth Derivative", "Second Deriv Notation", "f Double Prime", "d2y dx2 Notation", "Velocity from Position", "Acceleration", "Jerk", "Position Velocity Accel", "Speed vs Velocity", "Direction of Motion", "Speeding Up Slowing", "Higher Trig Derivatives"], "taxonomy_id": "HIGH", "hop_depth": 0}
+{"id": "calculus_T4_APPL", "domain": "calculus", "type": "T4_aggregate", "query": "List all APPL concepts in this knowledge graph", "ground_truth": ["Related Rates", "Related Rates Setup", "Implicit in Context", "Rate Variables", "Related Rates Diagram", "Ladder Problem", "Balloon Problem", "Shadow Problem", "Conical Tank Problem", "Distance Rate Problem", "Linear Approximation", "Tangent Line Approx", "Linearization Formula", "Error in Approximation", "Differential", "dy Notation", "dx Notation", "Differential Approx", "Marginal Analysis", "Marginal Cost", "Marginal Revenue", "Marginal Profit", "Economics Interpretation", "Units of Derivative", "Rate Interpretation", "Derivative in Context", "Population Rate", "Temperature Rate", "Concentration Rate", "L'Hospital's Rule", "L'Hospital Conditions", "Zero Over Zero Apply", "Inf Over Inf Apply", "Indeterminate Products", "Zero Times Infinity", "Indeterminate Powers", "One to Infinity", "Repeated L'Hospital", "Verify L'Hospital"], "taxonomy_id": "APPL", "hop_depth": 0}
+{"id": "calculus_T4_ANAL", "domain": "calculus", "type": "T4_aggregate", "query": "List all ANAL concepts in this knowledge graph", "ground_truth": ["Mean Value Theorem", "MVT Statement", "MVT Conditions", "MVT Conclusion", "Rolle's Theorem", "Rolle's Conditions", "MVT Applications", "Average vs Instant MVT", "Extreme Value Theorem", "EVT Statement", "EVT Conditions", "Global Maximum", "Global Minimum", "Local Maximum", "Local Minimum", "Critical Point", "Critical Number", "Where f Prime Zero", "Where f Prime DNE", "First Derivative Test", "Sign Chart", "Increasing Function", "Decreasing Function", "Monotonicity", "Sign Change Analysis", "Second Derivative Test", "Concavity", "Concave Up", "Concave Down", "Inflection Point", "Point of Inflection", "Candidates Test", "Closed Interval Method", "Endpoint Extrema"], "taxonomy_id": "ANAL", "hop_depth": 0}
+{"id": "calculus_T4_CURV", "domain": "calculus", "type": "T4_aggregate", "query": "List all CURV concepts in this knowledge graph", "ground_truth": ["Curve Sketching", "Complete Curve Analysis", "f f Prime f Dbl Prime", "Graph from Derivative", "Derivative from Graph", "Connecting Three Graphs", "Domain Analysis", "Intercept Analysis", "Symmetry Analysis", "Asymptote Analysis", "Increasing Decreasing", "Local Extrema Analysis", "Concavity Analysis", "Inflection Analysis"], "taxonomy_id": "CURV", "hop_depth": 0}
+{"id": "calculus_T4_OPT", "domain": "calculus", "type": "T4_aggregate", "query": "List all OPT concepts in this knowledge graph", "ground_truth": ["Optimization", "Optimization Problem", "Objective Function", "Constraint Equation", "Primary Equation", "Setting Up Optimization", "Maximizing Area", "Minimizing Distance", "Minimizing Cost", "Maximizing Volume", "Fencing Problem", "Box Problem", "Can Problem", "Closest Point Problem", "Maximum Profit", "Applied Optimization", "Verifying Maximum", "Verifying Minimum", "Second Deriv Verify", "Endpoint Consideration", "Practical Domain"], "taxonomy_id": "OPT", "hop_depth": 0}
+{"id": "calculus_T4_INTEG", "domain": "calculus", "type": "T4_aggregate", "query": "List all INTEG concepts in this knowledge graph", "ground_truth": ["Antiderivative", "Indefinite Integral", "Integral Notation", "Integrand", "Variable of Integration", "Constant of Integration", "General Antiderivative", "Particular Antideriv", "Power Rule Integration", "Constant Rule Integr", "Sum Rule Integration", "Difference Rule Integr", "Constant Multiple Integ", "Basic Trig Integrals", "Integral of Sin x", "Integral of Cos x", "Integral of Sec Squared", "Integral of Csc Squared", "Integral of Sec Tan", "Integral of Csc Cot", "Integral of e to x", "Integral of a to x", "Integral of 1 Over x", "Natural Log Integral", "Inverse Trig Integrals", "Arcsin Integral", "Arctan Integral", "Arcsec Integral"], "taxonomy_id": "INTEG", "hop_depth": 0}
+{"id": "calculus_T4_RIEM", "domain": "calculus", "type": "T4_aggregate", "query": "List all RIEM concepts in this knowledge graph", "ground_truth": ["Riemann Sum", "Left Riemann Sum", "Right Riemann Sum", "Midpoint Riemann Sum", "Trapezoidal Rule", "Summation Notation", "Sigma Notation", "Index of Summation", "Limit of Riemann Sum", "Definite Integral", "Definite Integral Notat", "Limits of Integration"], "taxonomy_id": "RIEM", "hop_depth": 0}
+{"id": "calculus_T4_FTC", "domain": "calculus", "type": "T4_aggregate", "query": "List all FTC concepts in this knowledge graph", "ground_truth": ["Fundamental Theorem", "FTC Part One", "FTC Part Two", "Evaluation Theorem", "Accumulation Function", "Integral as Function", "Derivative of Integral", "FTC Chain Rule", "Net Change Theorem", "Net Signed Area", "Area Under Curve", "Integral Properties", "Additivity Property", "Reversing Limits", "Zero Width Integral", "Integral of Sum", "Integral Bounds Split", "Comparison Property", "Even Function Integral", "Odd Function Integral", "Average Value", "Average Value Formula", "Mean Value Integral"], "taxonomy_id": "FTC", "hop_depth": 0}
+{"id": "calculus_T4_TECH", "domain": "calculus", "type": "T4_aggregate", "query": "List all TECH concepts in this knowledge graph", "ground_truth": ["u-Substitution", "Substitution Method", "Choosing u", "du Calculation", "Back Substitution", "Definite Substitution", "Changing Bounds", "Long Division Method", "Completing Square", "Partial Fractions", "Integration Strategy"], "taxonomy_id": "TECH", "hop_depth": 0}
+{"id": "calculus_T5_234_228", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Indeterminate Powers relate to L'Hospital's Rule?", "ground_truth": ["Indeterminate Powers", "L'Hospital's Rule"], "concept_id_a": 234, "concept_id_b": 228, "hop_depth": 1}
+{"id": "calculus_T5_55_24", "domain": "calculus", "type": "T5_cross_concept", "query": "How does One-Sided Continuity relate to One-Sided Limit?", "ground_truth": ["One-Sided Continuity", "One-Sided Limit"], "concept_id_a": 55, "concept_id_b": 24, "hop_depth": 1}
+{"id": "calculus_T5_374_371", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Back Substitution relate to Substitution Method?", "ground_truth": ["Back Substitution", "Substitution Method"], "concept_id_a": 374, "concept_id_b": 371, "hop_depth": 1}
+{"id": "calculus_T5_166_163", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Solving for dy dx relate to dy dx Implicitly?", "ground_truth": ["Solving for dy dx", "dy dx Implicitly"], "concept_id_a": 166, "concept_id_b": 163, "hop_depth": 1}
+{"id": "calculus_T5_198_132", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Higher Trig Derivatives relate to Derivative of Sine?", "ground_truth": ["Higher Trig Derivatives", "Derivative of Sine"], "concept_id_a": 198, "concept_id_b": 132, "hop_depth": 1}
+{"id": "calculus_T5_350_349", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Evaluation Theorem relate to FTC Part Two?", "ground_truth": ["Evaluation Theorem", "FTC Part Two"], "concept_id_a": 350, "concept_id_b": 349, "hop_depth": 1}
+{"id": "calculus_T5_150_98", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Leibniz Chain Rule relate to Leibniz Notation?", "ground_truth": ["Leibniz Chain Rule", "Leibniz Notation"], "concept_id_a": 150, "concept_id_b": 98, "hop_depth": 1}
+{"id": "calculus_T5_90_21", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Tangent Line relate to Limit?", "ground_truth": ["Tangent Line", "Limit"], "concept_id_a": 90, "concept_id_b": 21, "hop_depth": 1}
+{"id": "calculus_T5_339_335", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Trapezoidal Rule relate to Riemann Sum?", "ground_truth": ["Trapezoidal Rule", "Riemann Sum"], "concept_id_a": 339, "concept_id_b": 335, "hop_depth": 1}
+{"id": "calculus_T5_169_95", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Inverse Function Thm relate to Derivative Function?", "ground_truth": ["Inverse Function Thm", "Derivative Function"], "concept_id_a": 169, "concept_id_b": 95, "hop_depth": 1}
+{"id": "calculus_T5_286_253", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Optimization relate to Critical Point?", "ground_truth": ["Optimization", "Critical Point"], "concept_id_a": 286, "concept_id_b": 253, "hop_depth": 1}
+{"id": "calculus_T5_134_133", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Derivative of Tangent relate to Derivative of Cosine?", "ground_truth": ["Derivative of Tangent", "Derivative of Cosine", "Derivative of Sine"], "concept_id_a": 134, "concept_id_b": 133, "hop_depth": 1}
+{"id": "calculus_T5_69_12", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Continuity of Exp Log relate to Exponential Function?", "ground_truth": ["Continuity of Exp Log", "Exponential Function"], "concept_id_a": 69, "concept_id_b": 12, "hop_depth": 1}
+{"id": "calculus_T5_70_54", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Intermediate Value Thm relate to Continuity on Interval?", "ground_truth": ["Intermediate Value Thm", "Continuity on Interval"], "concept_id_a": 70, "concept_id_b": 54, "hop_depth": 1}
+{"id": "calculus_T5_305_271", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Endpoint Consideration relate to Endpoint Extrema?", "ground_truth": ["Endpoint Consideration", "Endpoint Extrema"], "concept_id_a": 305, "concept_id_b": 271, "hop_depth": 1}
+{"id": "calculus_T5_253_251", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Critical Point relate to Local Maximum?", "ground_truth": ["Critical Point", "Local Maximum", "Derivative Function"], "concept_id_a": 253, "concept_id_b": 251, "hop_depth": 1}
+{"id": "calculus_T5_300_220", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Maximum Profit relate to Marginal Profit?", "ground_truth": ["Maximum Profit", "Marginal Profit"], "concept_id_a": 300, "concept_id_b": 220, "hop_depth": 1}
+{"id": "calculus_T5_289_287", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Constraint Equation relate to Optimization Problem?", "ground_truth": ["Constraint Equation", "Optimization Problem"], "concept_id_a": 289, "concept_id_b": 287, "hop_depth": 1}
+{"id": "calculus_T5_334_331", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Arcsec Integral relate to Inverse Trig Integrals?", "ground_truth": ["Arcsec Integral", "Inverse Trig Integrals"], "concept_id_a": 334, "concept_id_b": 331, "hop_depth": 1}
+{"id": "calculus_T5_43_29", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Squeeze Theorem relate to Limit Laws?", "ground_truth": ["Squeeze Theorem", "Limit Laws"], "concept_id_a": 43, "concept_id_b": 29, "hop_depth": 1}
+{"id": "calculus_T5_70_56", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Intermediate Value Thm relate to Continuous Function?", "ground_truth": ["Intermediate Value Thm", "Continuous Function", "Continuity on Interval"], "concept_id_a": 70, "concept_id_b": 56, "hop_depth": 1}
+{"id": "calculus_T5_47_23", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Limits from Graphs relate to Intuitive Limit?", "ground_truth": ["Limits from Graphs", "Intuitive Limit"], "concept_id_a": 47, "concept_id_b": 23, "hop_depth": 1}
+{"id": "calculus_T5_284_264", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Concavity Analysis relate to Concavity?", "ground_truth": ["Concavity Analysis", "Concavity"], "concept_id_a": 284, "concept_id_b": 264, "hop_depth": 1}
+{"id": "calculus_T5_242_238", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Rolle's Theorem relate to Mean Value Theorem?", "ground_truth": ["Rolle's Theorem", "Mean Value Theorem"], "concept_id_a": 242, "concept_id_b": 238, "hop_depth": 1}
+{"id": "calculus_T5_77_72", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Behavior Near Asymptote relate to Vertical Asymptote?", "ground_truth": ["Behavior Near Asymptote", "Vertical Asymptote"], "concept_id_a": 77, "concept_id_b": 72, "hop_depth": 1}
+{"id": "calculus_T5_173_14", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Derivative of Arcsin relate to Trigonometric Function?", "ground_truth": ["Derivative of Arcsin", "Trigonometric Function"], "concept_id_a": 173, "concept_id_b": 14, "hop_depth": 1}
+{"id": "calculus_T5_135_134", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Derivative of Cotangent relate to Derivative of Tangent?", "ground_truth": ["Derivative of Cotangent", "Derivative of Tangent"], "concept_id_a": 135, "concept_id_b": 134, "hop_depth": 1}
+{"id": "calculus_T5_319_308", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Constant Multiple Integ relate to Indefinite Integral?", "ground_truth": ["Constant Multiple Integ", "Indefinite Integral"], "concept_id_a": 319, "concept_id_b": 308, "hop_depth": 1}
+{"id": "calculus_T5_96_95", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Derivative Notation relate to Derivative Function?", "ground_truth": ["Derivative Notation", "Derivative Function"], "concept_id_a": 96, "concept_id_b": 95, "hop_depth": 1}
+{"id": "calculus_T5_300_294", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Maximum Profit relate to Minimizing Cost?", "ground_truth": ["Maximum Profit", "Minimizing Cost"], "concept_id_a": 300, "concept_id_b": 294, "hop_depth": 1}
+{"id": "calculus_T5_129_127", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Quotient Rule relate to Product Rule?", "ground_truth": ["Quotient Rule", "Product Rule"], "concept_id_a": 129, "concept_id_b": 127, "hop_depth": 1}
+{"id": "calculus_T5_330_329", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Natural Log Integral relate to Integral of 1 Over x?", "ground_truth": ["Natural Log Integral", "Integral of 1 Over x"], "concept_id_a": 330, "concept_id_b": 329, "hop_depth": 1}
+{"id": "calculus_T5_174_173", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Derivative of Arccos relate to Derivative of Arcsin?", "ground_truth": ["Derivative of Arccos", "Derivative of Arcsin"], "concept_id_a": 174, "concept_id_b": 173, "hop_depth": 1}
+{"id": "calculus_T5_59_57", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Jump Discontinuity relate to Discontinuity?", "ground_truth": ["Jump Discontinuity", "Discontinuity"], "concept_id_a": 59, "concept_id_b": 57, "hop_depth": 1}
+{"id": "calculus_T5_314_313", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Particular Antideriv relate to General Antiderivative?", "ground_truth": ["Particular Antideriv", "General Antiderivative"], "concept_id_a": 314, "concept_id_b": 313, "hop_depth": 1}
+{"id": "calculus_T5_39_37", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Algebraic Limit Technique relate to Zero Over Zero Form?", "ground_truth": ["Algebraic Limit Technique", "Zero Over Zero Form", "Indeterminate Form"], "concept_id_a": 39, "concept_id_b": 37, "hop_depth": 1}
+{"id": "calculus_T5_10_3", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Polynomial Function relate to Function Notation?", "ground_truth": ["Polynomial Function", "Function Notation", "Function"], "concept_id_a": 10, "concept_id_b": 3, "hop_depth": 1}
+{"id": "calculus_T5_68_56", "domain": "calculus", "type": "T5_cross_concept", "query": "How does Continuity of Trig relate to Continuous Function?", "ground_truth": ["Continuity of Trig", "Continuous Function"], "concept_id_a": 68, "concept_id_b": 56, "hop_depth": 1}