id
stringlengths
22
32
setting_key
stringclasses
7 values
messages
listlengths
1
1
ground_truth
stringlengths
1
79
dataset
stringclasses
1 value
omega_config
stringclasses
7 values
omega_split
stringclasses
1 value
trans_prob_letter_test_022
trans_prob_letter
[ { "content": "How many distinct words of length 8 can be formed from {\"o\": 7,\"p\": 6,\"q\": 5,\"r\": 4}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63444
math
trans_prob_letter
test
trans_prob_letter_test_023
trans_prob_letter
[ { "content": "How many distinct words of length 9 can be formed from {\"s\": 8,\"t\": 7,\"u\": 6,\"v\": 5}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
259143
math
trans_prob_letter
test
trans_prob_letter_test_024
trans_prob_letter
[ { "content": "How many distinct words of length 12 can be formed from {\"a\": 11,\"b\": 10,\"c\": 9,\"d\": 8,\"e\": 7}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
243982380
math
trans_prob_letter
test
trans_prob_letter_test_025
trans_prob_letter
[ { "content": "How many distinct words of length 10 can be formed from {\"f\": 9,\"g\": 8,\"h\": 7,\"i\": 6,\"j\": 5}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
9694180
math
trans_prob_letter
test
trans_prob_letter_test_026
trans_prob_letter
[ { "content": "How many distinct words of length 11 can be formed from {\"k\": 10,\"l\": 9,\"m\": 8,\"n\": 7,\"o\": 6}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
48719704
math
trans_prob_letter
test
trans_prob_letter_test_027
trans_prob_letter
[ { "content": "How many distinct words of length 8 can be formed from {\"p\": 7,\"q\": 6,\"r\": 5,\"s\": 4,\"t\": 3}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
364060
math
trans_prob_letter
test
trans_prob_letter_test_028
trans_prob_letter
[ { "content": "How many distinct words of length 9 can be formed from {\"u\": 8,\"v\": 7,\"w\": 6,\"x\": 5,\"y\": 4}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1908240
math
trans_prob_letter
test
trans_prob_letter_test_029
trans_prob_letter
[ { "content": "How many distinct words of length 7 can be formed from {\"z\": 6,\"a\": 5,\"b\": 4,\"c\": 3,\"d\": 2}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
63595
math
trans_prob_letter
test
trans_prob_letter_test_030
trans_prob_letter
[ { "content": "How many distinct words of length 6 can be formed from {\"e\": 5,\"f\": 4,\"g\": 3,\"h\": 2,\"i\": 1}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
8634
math
trans_prob_letter
test
trans_prob_letter_test_031
trans_prob_letter
[ { "content": "How many distinct words of length 5 can be formed from {\"j\": 4,\"k\": 3,\"l\": 2,\"m\": 1,\"n\": 1}? (value indicates the number of letters)\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
1410
math
trans_prob_letter
test
trans_integrations_test_000
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{x + \\sqrt{x}}{1 + \\sqrt{x}} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{2}{3}x^{3/2}
math
trans_integrations
test
trans_integrations_test_001
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{e^{x+1}}{e^x + 1} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
e \log(e^x + 1)
math
trans_integrations
test
trans_integrations_test_002
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\sqrt[3]{3 \\sin(x) - \\sin(3x)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
-\frac{\sqrt{3}}{4} \cos(x)
math
trans_integrations
test
trans_integrations_test_003
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{x \\log(x) \\cos(x) - \\sin(x)}{x \\log^2(x)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{\sin(x)}{\log(x)}
math
trans_integrations
test
trans_integrations_test_004
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\sqrt[3]{\\frac{x}{4/2}} \\sqrt{\\frac{x}{5/3}} \\sqrt[4]{x^{6/\\sqrt{4}}} \\cdots dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{x^2}{2}
math
trans_integrations
test
trans_integrations_test_005
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{e^{2x}}{(x^2 + x)(xe^x)^4 + 1} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{1}{2} \arctan(x^2 e^{2x})
math
trans_integrations
test
trans_integrations_test_006
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (\\sec^4(x) - \\tan^4(x)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2 \tan(x) - x
math
trans_integrations
test
trans_integrations_test_007
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{\\sin(4x) \\cos(x)}{\\cos(2x) \\sin(x)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2x + \sin(2x)
math
trans_integrations
test
trans_integrations_test_008
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\sin(x) \\sinh(x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{1}{2}(\sin(x) \cosh(x) - \cos(x) \sinh(x))
math
trans_integrations
test
trans_integrations_test_009
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{\\cos(x) + \\cos(x + \\frac{2\\pi}{3}) + \\cos(x - \\frac{2\\pi}{3})}{2} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
math
trans_integrations
test
trans_integrations_test_010
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{(x - 1)\\log(x+1)}{(x + 1)\\log(x-1)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
x
math
trans_integrations
test
trans_integrations_test_011
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (x \\log x + 2x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{1}{2}x^2 \log x + \frac{3}{4}x^2
math
trans_integrations
test
trans_integrations_test_012
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{dx}{x \\log x + 2x}. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\log(\log x + 2)
math
trans_integrations
test
trans_integrations_test_013
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{\\cos x + \\cot x + \\csc x + 1}{\\sin x + \\tan x + \\sec x + 1} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\log(\sin x)
math
trans_integrations
test
trans_integrations_test_014
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{x^{2024} - 1}{x^{506} - 1} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
x + \frac{x^{507}}{507} + \frac{x^{1013}}{1013} + \frac{x^{1519}}{1519}
math
trans_integrations
test
trans_integrations_test_015
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\csc^2(x) \\tan^{2024}(x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{\tan^{2023}(x)}{2023}
math
trans_integrations
test
trans_integrations_test_016
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\cos^x(x)(\\log(\\cos x) - x \\tan x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\cos^x(x)
math
trans_integrations
test
trans_integrations_test_017
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (x + 1 - e^{-x})e^{xe^x} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
e^{(e^x-1)x}
math
trans_integrations
test
trans_integrations_test_018
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\left(\\frac{\\arctan(x)}{1 - x^2} + \\frac{\\text{arctanh}(x)}{1 + x^2}\\right) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\arctan(x)\text{arctanh}(x)
math
trans_integrations
test
trans_integrations_test_019
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\sum_{k=0}^{\\infty} \\sin\\left(\\frac{k\\pi}{2}\\right) \\frac{x^k}{k!} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{\log(x^2 + 1)}{2}
math
trans_integrations
test
trans_integrations_test_020
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{x^4}{3 - 6x + 6x^2 - 4x^3 + 2x^4} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{x^2}{2} + \frac{1}{4}\log(3 - 6x + 6x^2 - 4x^3 + 2x^4)
math
trans_integrations
test
trans_integrations_test_021
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int x^{\\frac{1}{\\log x}} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
ex
math
trans_integrations
test
trans_integrations_test_022
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\text{sech}(x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2 \arctan(e^x)
math
trans_integrations
test
trans_integrations_test_023
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{e^x}{(1 + e^x) \\log(1 + e^x)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\log(\log(1 + e^x))
math
trans_integrations
test
trans_integrations_test_024
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (1 + x + x^2 + x^3 + x^4)(1 - x + x^2 - x^3 + x^4) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
x + \frac{x^3}{3} + \frac{x^5}{5} + \frac{x^7}{7} + \frac{x^9}{9}
math
trans_integrations
test
trans_integrations_test_025
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (x + \\sin(x) + x \\cos(x) + \\sin(x) \\cos(x)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{(x + \sin(x))^2}{2}
math
trans_integrations
test
trans_integrations_test_026
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (\\sin^2(x) + \\cos^2(x) + \\tan^2(x) + \\cot^2(x) + \\sec^2(x) + \\csc^2(x)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
2 \tan(x) - 2 \cot(x) - x
math
trans_integrations
test
trans_integrations_test_027
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (2 \\log x + 1)e^{(\\log x)^2} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
xe^{(\log x)^2}
math
trans_integrations
test
trans_integrations_test_028
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int ((1 - x)^3 + (x - x^2)^3 + (x^2 - 1)^3 - 3(1 - x)(x - x^2)(x^2 - 1)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
0
math
trans_integrations
test
trans_integrations_test_029
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (\\sin^6 x + \\cos^6 x + 3 \\sin^2 x \\cos^2 x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
x
math
trans_integrations
test
trans_integrations_test_030
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (x + e + 1)^x e^{ex} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
x^{e+1}e^x
math
trans_integrations
test
trans_integrations_test_031
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{1 + 2x^{2022}}{x + x^{2023}} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{1}{2022} \log(x^{2022} + x^{4044})
math
trans_integrations
test
trans_integrations_test_032
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int (3 \\sin(20x) \\cos(23x) + 20 \\sin(43x)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\sin(20x) \sin(23x)
math
trans_integrations
test
trans_integrations_test_033
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{\\sin x}{2e^x + \\cos x + \\sin x} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{x - \log(2e^x + \cos x + \sin x)}{2}
math
trans_integrations
test
trans_integrations_test_034
trans_integrations
[ { "content": "Evaluate the indefinite integral \\int \\frac{\\log(x/\\pi)}{(\\log x)^{\\log(\\pi e)}} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user" } ]
\frac{x}{(\log x)^{\log \pi}}
math
trans_integrations
test
trans_gridworld_test_000
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of an 8x8 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main dia...
3
math
trans_gridworld
test
trans_gridworld_test_001
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 10x10 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
4
math
trans_gridworld
test
trans_gridworld_test_002
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 12x12 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
5
math
trans_gridworld
test
trans_gridworld_test_003
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 14x14 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
6
math
trans_gridworld
test
trans_gridworld_test_004
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 16x16 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
7
math
trans_gridworld
test
trans_gridworld_test_005
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of an 18x18 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main d...
8
math
trans_gridworld
test
trans_gridworld_test_006
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 20x20 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
9
math
trans_gridworld
test
trans_gridworld_test_007
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 22x22 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
10
math
trans_gridworld
test
trans_gridworld_test_008
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 24x24 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
11
math
trans_gridworld
test
trans_gridworld_test_009
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 26x26 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
12
math
trans_gridworld
test
trans_gridworld_test_010
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 28x28 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
13
math
trans_gridworld
test
trans_gridworld_test_011
trans_gridworld
[ { "content": "Suppose you have an agent in the bottom left (i=0, j=0) cell of a 30x30 grid, whose objective is to make it to the top right cell. Its valid moves from any cell are to move one cell to the right, or to move one cell upward, and it is further constrained by having to stay strictly below the main di...
14
math
trans_gridworld
test
trans_gridworld_test_012
trans_gridworld
[ { "content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8)...
10
math
trans_gridworld
test
trans_gridworld_test_013
trans_gridworld
[ { "content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (2, 0), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, ...
20
math
trans_gridworld
test
trans_gridworld_test_014
trans_gridworld
[ { "content": "In a 10x10 grid, how many different paths are there from the bottom left (0, 0) to the top right (9, 9), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8)?\n\nPre...
2860
math
trans_gridworld
test
trans_gridworld_test_015
trans_gridworld
[ { "content": "In a 20x20 grid, how many different paths are there from the bottom left (0, 0) to the top right (19, 19), if you can only move right or up at each step, subject to the constraint that you cannot move through the following cells: (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6), (7, 7), (8, 8), (9, ...
955277400
math
trans_gridworld
test
trans_circles_test_000
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
2.41
math
trans_circles
test
trans_circles_test_001
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
1.73
math
trans_circles
test
trans_circles_test_002
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
4.41
math
trans_circles
test
trans_circles_test_003
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
3.14
math
trans_circles
test
trans_circles_test_004
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
11.24
math
trans_circles
test
trans_circles_test_005
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
8.2
math
trans_circles
test
trans_circles_test_006
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
74.84
math
trans_circles
test
trans_circles_test_007
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
56.91
math
trans_circles
test
trans_circles_test_008
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
2469.74
math
trans_circles
test
trans_circles_test_009
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
1889.88
math
trans_circles
test
trans_circles_test_010
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
2
math
trans_circles
test
trans_circles_test_011
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
3
math
trans_circles
test
trans_circles_test_012
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
5
math
trans_circles
test
trans_circles_test_013
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
10
math
trans_circles
test
trans_circles_test_014
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
20
math
trans_circles
test
trans_circles_test_015
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
2
math
trans_circles
test
trans_circles_test_016
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
4
math
trans_circles
test
trans_circles_test_017
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
16
math
trans_circles
test
trans_circles_test_018
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
512
math
trans_circles
test
trans_circles_test_019
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through the center of C_1. Likewise,...
524288
math
trans_circles
test
trans_circles_test_020
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
2.61
math
trans_circles
test
trans_circles_test_021
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
5.12
math
trans_circles
test
trans_circles_test_022
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
20.38
math
trans_circles
test
trans_circles_test_023
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
652
math
trans_circles
test
trans_circles_test_024
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through A_1 and B_1. Likewise, draw ...
667544
math
trans_circles
test
trans_circles_test_025
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
0.41
math
trans_circles
test
trans_circles_test_026
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
1.58
math
trans_circles
test
trans_circles_test_027
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
2.75
math
trans_circles
test
trans_circles_test_028
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
12.84
math
trans_circles
test
trans_circles_test_029
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
423.74
math
trans_circles
test
trans_circles_test_030
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
0.41
math
trans_circles
test
trans_circles_test_031
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
0.41
math
trans_circles
test
trans_circles_test_032
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
0.41
math
trans_circles
test
trans_circles_test_033
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
0.41
math
trans_circles
test
trans_circles_test_034
trans_circles
[ { "content": "Let circle C_1 be positioned in the coordinate plane with a radius of 1 and its center on the y-axis. Draw its horizontal diameter and call its endpoints A_1 and B_1. Draw its vertical diameter and call the higher endpoint D_1. Then, let circle C_2 be the circle centered at D_1 that passes through...
0.41
math
trans_circles
test