{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"cc4a80e6-d8cc-5977-96b4-15b33e8c43ea","task_key":"geometry--test--cc4a80e6-d8cc-5977-96b4-15b33e8c43ea","task_revision_id":"1","upstream_id":"","short_description":"A quarter-circle of radius 3 units is drawn at each of the vertices of a square…","config":"geometry","split":"test","body":"{\"level\":\"Level 2\",\"problem\":\"A quarter-circle of radius 3 units is drawn at each of the vertices of a square with sides of 6 units. [asy]\\n\\ndraw((0,0)--(0,1)--(1,1)--(1,0),black);\\n\\nfill((0,0)--(0,1)--(1,1)--(1,0)--cycle,black);\\n\\nfill((0.5,1){down}..{left}(0,0.5)--(0,1)--(0.5,1)--cycle,white);\\n\\nfill((0.5,1){down}..{right}(1,0.5)--(1,1)--(0.5,1)--cycle,white);\\n\\nfill((0.5,0){up}..{left}(0,0.5)--(0,0)--(0.5,0)--cycle,white);\\n\\nfill((0.5,0){up}..{right}(1,0.5)--(1,0)--(0.5,0)--cycle,white);\\n\\n[/asy] The area of the shaded region can be expressed in the form $a-b\\\\pi$ square units, where $a$ and $b$ are both integers. What is the value of $a+b?$\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}