{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (3(-5(-2|((1(-3x + 2) + 2)/(2(-3x + 2) + 1)) - 2| - 1)^2 - 2(-2|((1(-3x + 2) + 2)/(2(-3x + 2) + 1)) - 2| - 1) - 5) - 1)/(1(-5(-2|((1(-3x + 2) + 2)/(2(-3x + 2) + 1)) - 2| - 1)^2 - 2(-2|((1(-3x + 2) + 2)/(2(-3x + 2) + 1)) - 2| - 1) - 5) - 3) and g(x) = 1|(-1e^(2(-2((2x - 2)/(-1x - 2))^2 + 3((2x - 2)/(-1x - 2)) + 3)))| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -5((2(4(5(5x - 3) + 1)^2 - 4(5(5x - 3) + 1) + 1) + 1)/(-1(4(5(5x - 3) + 1)^2 - 4(5(5x - 3) + 1) + 1) + 2)) + 5 and g(x) = 3|(-1(2(-3e^(1x) - 2) - 5) + 3) + 2| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2|(1(-5(3((-3x + 3)/(-2x + 3))^2 + 2((-3x + 3)/(-2x + 3)) + 1)^2 - 2(3((-3x + 3)/(-2x + 3))^2 + 2((-3x + 3)/(-2x + 3)) + 1) + 3) + 5) + 2| - 1 and g(x) = 3(-3(3|(-3cos(1\u03c0x + 2) + 1) + 2| + 2) - 1) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1(-1|(-2((-1(1cos(3\u03c0x)) + 3)/(-2(1cos(3\u03c0x)) + 3)) + 4) - 3| + 3) - 5 and g(x) = (-3(-4((1((-1x)/(-3x - 2)) + 1)/(-1((-1x)/(-3x - 2)) + 3)) + 2) + 1)/(-2(-4((1((-1x)/(-3x - 2)) + 1)/(-1((-1x)/(-3x - 2)) + 3)) + 2) + 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(-1((-3(1((2x - 1)/(1x - 2)) + 2) - 2)/(1(1((2x - 1)/(1x - 2)) + 2) + 1)) - 1) - 3| + 2 and g(x) = (-2(-1((3((1x + 2)/(1x + 3)) - 2)/(1((1x + 2)/(1x + 3)) + 3)) + 5) + 1)/(-1(-1((3((1x + 2)/(1x + 3)) - 2)/(1((1x + 2)/(1x + 3)) + 3)) + 5) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2cos(1\u03c0(3(-2(-2(-5x)^2 - 3(-5x) + 4) - 4)^2 - 2(-2(-2(-5x)^2 - 3(-5x) + 4) - 4) + 4) - 1) + 3 and g(x) = -3e^(-1(-5(-3((-2x + 1)/(-1x + 3))^2 - 4((-2x + 1)/(-1x + 3)) + 5) - 3)) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (2(-4((1((2(2x + 2) - 1)/(3(2x + 2) - 1)) - 3)/(-1((2(2x + 2) - 1)/(3(2x + 2) - 1)) + 2)) - 1) - 3)/(-3(-4((1((2(2x + 2) - 1)/(3(2x + 2) - 1)) - 3)/(-1((2(2x + 2) - 1)/(3(2x + 2) - 1)) + 2)) - 1) - 1) and g(x) = (3(-5((2(4x^2 + 4x + 3) + 1)/(1(4x^2 + 4x + 3) + 3)) + 2) + 1)/(2(-5((2(4x^2 + 4x + 3) + 1)/(1(4x^2 + 4x + 3) + 3)) + 2) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(-4(-2(-4(-1|x + 2|)^2 - 1(-1|x + 2|) + 2) - 3) - 5) + 1 and g(x) = (-1(3(-3((1x + 2)/(-1x - 2)) + 2)^2 + 2(-3((1x + 2)/(-1x - 2)) + 2) + 2))/(-3(3(-3((1x + 2)/(-1x - 2)) + 2)^2 + 2(-3((1x + 2)/(-1x - 2)) + 2) + 2) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(4(5(1|(2|x + 3|) + 1| + 3) - 5) + 2) + 5 and g(x) = -2e^(-2(-3(5(-3x + 3)^2 + 4(-3x + 3) + 1) + 5)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1|((-1(-5((-2(5x - 4) - 2)/(1(5x - 4) - 2)) - 1))/(3(-5((-2(5x - 4) - 2)/(1(5x - 4) - 2)) - 1) - 1)) + 1| + 1 and g(x) = -1|((1(-3cos(2\u03c0(-5x + 5) - 1) - 2) + 2)/(-3(-3cos(2\u03c0(-5x + 5) - 1) - 2) + 2)) + 1| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -5(3|(1e^(1(2|((3x - 3)/(-1x + 2)) - 1| - 3)) + 2) + 1| + 2)^2 + 1(3|(1e^(1(2|((3x - 3)/(-1x + 2)) - 1| - 3)) + 2) + 1| + 2) - 1 and g(x) = -3|(-3|(2e^(-2(-3|x| - 1)) + 1) + 3|) + 1| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3((-1((-1(1(1e^(1x) - 3) + 3) + 2)/(2(1(1e^(1x) - 3) + 3) - 1)))/(-2((-1(1(1e^(1x) - 3) + 3) + 2)/(2(1(1e^(1x) - 3) + 3) - 1)) + 3))^2 + 2((-1((-1(1(1e^(1x) - 3) + 3) + 2)/(2(1(1e^(1x) - 3) + 3) - 1)))/(-2((-1(1(1e^(1x) - 3) + 3) + 2)/(2(1(1e^(1x) - 3) + 3) - 1)) + 3)) - 2 and g(x) = -1(-2|(1cos(3\u03c0(3x^2 + 1x + 1) - 2)) + 1| - 2) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 4(-1(-2((-1(-1x))/(-3(-1x) + 1))^2 - 3((-1(-1x))/(-3(-1x) + 1)) - 5)^2 + 3(-2((-1(-1x))/(-3(-1x) + 1))^2 - 3((-1(-1x))/(-3(-1x) + 1)) - 5) + 4) + 1 and g(x) = -1|((1(3|(-2|x| + 1) + 2|) + 2)/(2(3|(-2|x| + 1) + 2|) - 1)) - 3| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -2e^(-1(-1(1((2((2x - 3)/(2x - 3)) - 2)/(-3((2x - 3)/(2x - 3)))) + 5)^2 + 3(1((2((2x - 3)/(2x - 3)) - 2)/(-3((2x - 3)/(2x - 3)))) + 5) - 5)) + 3 and g(x) = -5(-5(1|(5x - 1) - 1| + 2)^2 - 3(1|(5x - 1) - 1| + 2))^2 - 2(-5(1|(5x - 1) - 1| + 2)^2 - 3(1|(5x - 1) - 1| + 2)) + 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -1|(-4((2(5((-3x - 1)/(-2x)) - 3))/(-1(5((-3x - 1)/(-2x)) - 3) - 1))^2 - 4((2(5((-3x - 1)/(-2x)) - 3))/(-1(5((-3x - 1)/(-2x)) - 3) - 1)) - 5)| - 1 and g(x) = -5(1(1|(-2|x|) - 1| + 1) - 4)^2 - 4(1(1|(-2|x|) - 1| + 1) - 4) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1(1((1(3(3|x + 3| + 2) - 2) + 1)/(-2(3(3|x + 3| + 2) - 2) + 3))^2 - 3((1(3(3|x + 3| + 2) - 2) + 1)/(-2(3(3|x + 3| + 2) - 2) + 3)) - 3) - 1)/(-1(1((1(3(3|x + 3| + 2) - 2) + 1)/(-2(3(3|x + 3| + 2) - 2) + 3))^2 - 3((1(3(3|x + 3| + 2) - 2) + 1)/(-2(3(3|x + 3| + 2) - 2) + 3)) - 3)) and g(x) = 4(5(1(1sin(2\u03c0x + 3) - 3) - 2) + 2) + 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 4(1sin(1\u03c0((3(1(4x + 1)^2 + 1) + 3)/(3(1(4x + 1)^2 + 1) + 2)) - 1) - 1)^2 - 2(1sin(1\u03c0((3(1(4x + 1)^2 + 1) + 3)/(3(1(4x + 1)^2 + 1) + 2)) - 1) - 1) + 2 and g(x) = (1(3|(2(-1x + 5) + 4) + 2| - 1) + 3)/(3(3|(2(-1x + 5) + 4) + 2| - 1)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 5(2|((3(3e^(-1(2x^2 - 2x + 2)) + 3) + 3)/(3(3e^(-1(2x^2 - 2x + 2)) + 3)))| - 2)^2 - 1(2|((3(3e^(-1(2x^2 - 2x + 2)) + 3) + 3)/(3(3e^(-1(2x^2 - 2x + 2)) + 3)))| - 2) - 2 and g(x) = (1(2(2(1x - 4) + 4)^2 + 4(2(1x - 4) + 4) + 1) + 1)/(3(2(2(1x - 4) + 4)^2 + 4(2(1x - 4) + 4) + 1) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 2(3(2e^(-2(2(2|x|) - 4)))^2 - 1(2e^(-2(2(2|x|) - 4))))^2 + 2(3(2e^(-2(2(2|x|) - 4)))^2 - 1(2e^(-2(2(2|x|) - 4)))) and g(x) = 3e^(-1((1((-1(2|x - 2| + 2) + 3)/(-3(2|x - 2| + 2) + 4)))/(-2((-1(2|x - 2| + 2) + 3)/(-3(2|x - 2| + 2) + 4))))) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 2((1(3sin(3\u03c0((3(-2x + 5) + 1)/(-2(-2x + 5) + 3)) + 3) - 3))/(1(3sin(3\u03c0((3(-2x + 5) + 1)/(-2(-2x + 5) + 3)) + 3) - 3) + 3)) and g(x) = 3|(-5(4(-5x) - 2)^2 - 1(4(-5x) - 2) - 5)| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-3(-1(3|(-2|x - 2| + 1) + 2|) - 1) - 3) + 4 and g(x) = -1(-3|(5(4x - 2) + 4)| - 2)^2 - 2(-3|(5(4x - 2) + 4)| - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 4(3(-3(-1|((-1x - 1)/(-3x - 3)) + 2|) - 4)^2 - 4(-3(-1|((-1x - 1)/(-3x - 3)) + 2|) - 4)) + 4 and g(x) = 3((-2((-3(1|x| - 2) - 3)/(-1(1|x| - 2) - 2)))/(2((-3(1|x| - 2) - 3)/(-1(1|x| - 2) - 2)) + 1)) - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 3(-2(-4(1(3sin(2\u03c0x - 1) + 2)^2 + 4(3sin(2\u03c0x - 1) + 2) + 5)^2 - 2(1(3sin(2\u03c0x - 1) + 2)^2 + 4(3sin(2\u03c0x - 1) + 2) + 5) + 2)^2 + 1(-4(1(3sin(2\u03c0x - 1) + 2)^2 + 4(3sin(2\u03c0x - 1) + 2) + 5)^2 - 2(1(3sin(2\u03c0x - 1) + 2)^2 + 4(3sin(2\u03c0x - 1) + 2) + 5) + 2) + 2) and g(x) = -2|(1e^(-2(-3(3x + 1) + 3)) - 2) - 3| - 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(2|((-3(-3|((-2x + 2)/(1x - 2)) + 3| + 2) - 3)/(3(-3|((-2x + 2)/(1x - 2)) + 3| + 2) + 1))| - 2) + 3)/(1(2|((-3(-3|((-2x + 2)/(1x - 2)) + 3| + 2) - 3)/(3(-3|((-2x + 2)/(1x - 2)) + 3| + 2) + 1))| - 2) - 3) and g(x) = 5((3((3(-1cos(2\u03c0x - 3) - 3) - 2)/(3(-1cos(2\u03c0x - 3) - 3) - 2)) - 1)/(-1((3(-1cos(2\u03c0x - 3) - 3) - 2)/(3(-1cos(2\u03c0x - 3) - 3) - 2)) + 3)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the third x-coordinate (rounded to the nearest integer) where f(x) = (-1((-3(-2|(-3(3|x - 2| + 3) + 2)|) - 3)/(-1(-2|(-3(3|x - 2| + 3) + 2)|) + 2)) - 3)/(2((-3(-2|(-3(3|x - 2| + 3) + 2)|) - 3)/(-1(-2|(-3(3|x - 2| + 3) + 2)|) + 2)) + 3) and g(x) = 2|(-1|(2e^(-1(1x + 5))) - 2| + 2)| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(1|((-1(-1e^(-1(-4x + 2)) - 1) - 3)/(1(-1e^(-1(-4x + 2)) - 1) - 2)) - 2|) + 3| and g(x) = 4(-5((2((1x - 3)/(-2x - 3)) - 3)/(1((1x - 3)/(-2x - 3)) + 1))^2 - 4((2((1x - 3)/(-2x - 3)) - 3)/(1((1x - 3)/(-2x - 3)) + 1)) + 4) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|((-2((2(3|(-3x^2 + 3x - 4) - 1| - 2) - 3)/(-1(3|(-3x^2 + 3x - 4) - 1| - 2) - 2)) + 2)/(-1((2(3|(-3x^2 + 3x - 4) - 1| - 2) - 3)/(-1(3|(-3x^2 + 3x - 4) - 1| - 2) - 2)) - 1)) + 1| - 2 and g(x) = -1|((2(-2((-1x + 2)/(1x + 1)) - 5) - 1)/(-2(-2((-1x + 2)/(1x + 1)) - 5))) - 1| + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -2(-1(5((2((3x + 3)/(1x)) + 1)/(-3((3x + 3)/(1x)) - 1)) - 4) - 4) + 4 and g(x) = 1|((-3(-1((2x + 2)/(-2x - 3)) + 4) - 2)/(-1(-1((2x + 2)/(-2x - 3)) + 4))) - 1| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 4(1(-1|(-1|(-1x^2 + 3x - 1) - 1|) - 3| + 3) + 2) - 5 and g(x) = (-3(-1cos(3\u03c0((-2(1|x - 2| - 1) - 2)/(-2(1|x - 2| - 1) - 2)) + 2) + 3) + 2)/(-2(-1cos(3\u03c0((-2(1|x - 2| - 1) - 2)/(-2(1|x - 2| - 1) - 2)) + 2) + 3)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 3(2(1(-2|(-5x^2 + 3x + 1) - 1| - 1)^2 + 5(-2|(-5x^2 + 3x + 1) - 1| - 1) - 3) - 4) + 2 and g(x) = (-2(3((1(-2|x + 1| - 1) + 3)/(-1(-2|x + 1| - 1) - 2)) - 1) - 1)/(1(3((1(-2|x + 1| - 1) + 3)/(-1(-2|x + 1| - 1) - 2)) - 1)) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (3(5((-2(-1(-1|x - 3|) + 2) + 1)/(-2(-1(-1|x - 3|) + 2) + 1)) - 2) - 3)/(2(5((-2(-1(-1|x - 3|) + 2) + 1)/(-2(-1(-1|x - 3|) + 2) + 1)) - 2) - 1) and g(x) = (2(-5(-2e^(1(-2|x - 3| + 2)) + 3) - 3) - 2)/(3(-5(-2e^(1(-2|x - 3| + 2)) + 3) - 3) + 2) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -1|(2|((3(3|((2x - 2)/(-3x - 2)) + 1|) + 2)/(-3(3|((2x - 2)/(-3x - 2)) + 1|))) + 1| - 1) + 1| + 1 and g(x) = (-2((1(1|(-4x^2 + 5) + 2| + 1) + 2)/(2(1|(-4x^2 + 5) + 2| + 1) + 1)) + 3)/(-1((1(1|(-4x^2 + 5) + 2| + 1) + 2)/(2(1|(-4x^2 + 5) + 2| + 1) + 1)) - 1) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-11", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3((2((2(-3(2x + 5) - 3) + 3)/(-1(-3(2x + 5) - 3))) + 1)/(1((2(-3(2x + 5) - 3) + 3)/(-1(-3(2x + 5) - 3))))) - 3)/(-3((2((2(-3(2x + 5) - 3) + 3)/(-1(-3(2x + 5) - 3))) + 1)/(1((2(-3(2x + 5) - 3) + 3)/(-1(-3(2x + 5) - 3))))) - 2) and g(x) = (3((2(-1(5x - 1) + 4))/(-1(-1(5x - 1) + 4))) + 3)/(-1((2(-1(5x - 1) + 4))/(-1(-1(5x - 1) + 4))) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (1(-2|(3|((-1(2x + 2) - 3)/(3(2x + 2))) + 1| + 1) - 3| - 3) - 1)/(-2(-2|(3|((-1(2x + 2) - 3)/(3(2x + 2))) + 1| + 1) - 3| - 3)) and g(x) = -2|(-3|((3(5x + 1))/(-2(5x + 1) - 1))| + 2) - 1| + 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(1|(2(-4(-3x - 1) + 5) + 4) - 2| + 1) - 2 and g(x) = (-3((-2(-3|(3x^2 - 5x - 3) + 1| - 1) + 2)/(-2(-3|(3x^2 - 5x - 3) + 1| - 1) - 2)) - 2)/(-3((-2(-3|(3x^2 - 5x - 3) + 1| - 1) + 2)/(-2(-3|(3x^2 - 5x - 3) + 1| - 1) - 2))) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 4(1|(1(-1e^(1(3x^2 + 4x + 2)) + 3) + 5) - 1| - 2)^2 + 3(1|(1(-1e^(1(3x^2 + 4x + 2)) + 3) + 5) - 1| - 2) - 2 and g(x) = -1((1(2|(2x^2 + 1x - 5) + 3| - 1) - 3)/(1(2|(2x^2 + 1x - 5) + 3| - 1) - 2)) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3(2|((-3(-3sin(2\u03c0(-3x) + 1) + 2) + 1)/(1(-3sin(2\u03c0(-3x) + 1) + 2) - 3)) - 3| + 2) - 3 and g(x) = -4(-2((1(5x^2 + 4x - 2) + 1)/(2(5x^2 + 4x - 2) + 1)) - 2) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (2((1((-1(-3(3x^2 - 1x - 2)) - 3)/(2(-3(3x^2 - 1x - 2)))) + 2)/(1((-1(-3(3x^2 - 1x - 2)) - 3)/(2(-3(3x^2 - 1x - 2)))) + 3)) + 2)/(-2((1((-1(-3(3x^2 - 1x - 2)) - 3)/(2(-3(3x^2 - 1x - 2)))) + 2)/(1((-1(-3(3x^2 - 1x - 2)) - 3)/(2(-3(3x^2 - 1x - 2)))) + 3))) and g(x) = (2(-2|(-2|(1e^(1x) + 1) + 2| + 2) - 1| + 1) + 3)/(-2(-2|(-2|(1e^(1x) + 1) + 2| + 2) - 1| + 1) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2(-2|(-3|(-1((-1x + 1)/(-2x + 3)) - 2) + 3| - 3) - 2| + 3) + 4 and g(x) = -1(-4((-2(-1x^2 - 5x + 5) + 2)/(-1(-1x^2 - 5x + 5) - 1)) - 1) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1((-1(-5(3e^(1((3x - 2)/(-2x - 1))))^2 + 5(3e^(1((3x - 2)/(-2x - 1)))) - 3) + 2)/(1(-5(3e^(1((3x - 2)/(-2x - 1))))^2 + 5(3e^(1((3x - 2)/(-2x - 1)))) - 3)))^2 - 5((-1(-5(3e^(1((3x - 2)/(-2x - 1))))^2 + 5(3e^(1((3x - 2)/(-2x - 1)))) - 3) + 2)/(1(-5(3e^(1((3x - 2)/(-2x - 1))))^2 + 5(3e^(1((3x - 2)/(-2x - 1)))) - 3))) + 3 and g(x) = (-1((-1(1(-2|x - 1| + 2)^2 - 4(-2|x - 1| + 2) - 3) + 3)/(-3(1(-2|x - 1| + 2)^2 - 4(-2|x - 1| + 2) - 3) - 1)) + 1)/(1((-1(1(-2|x - 1| + 2)^2 - 4(-2|x - 1| + 2) - 3) + 3)/(-3(1(-2|x - 1| + 2)^2 - 4(-2|x - 1| + 2) - 3) - 1))) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(-1(1|(-2(-4x + 2)) + 2| + 1)^2 - 3(1|(-2(-4x + 2)) + 2| + 1) - 4)^2 - 2(-1(1|(-2(-4x + 2)) + 2| + 1)^2 - 3(1|(-2(-4x + 2)) + 2| + 1) - 4) - 4 and g(x) = -4(3|(3(-2x^2 + 2) - 1) + 1| - 2) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-2(1(-3|((-1(-1sin(1\u03c0x + 2) + 3) + 1)/(-2(-1sin(1\u03c0x + 2) + 3) - 2)) + 1| + 1) - 5) - 3)/(-2(1(-3|((-1(-1sin(1\u03c0x + 2) + 3) + 1)/(-2(-1sin(1\u03c0x + 2) + 3) - 2)) + 1| + 1) - 5) - 3) and g(x) = (3((1(5((-1x + 2)/(1x + 1)) + 2) - 1)/(-1(5((-1x + 2)/(1x + 1)) + 2) - 1)) - 2)/(2((1(5((-1x + 2)/(1x + 1)) + 2) - 1)/(-1(5((-1x + 2)/(1x + 1)) + 2) - 1)) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2e^(2((1(2((-3(-1|x - 1| + 2) + 3)/(-1(-1|x - 1| + 2) + 2)) + 1))/(-2(2((-3(-1|x - 1| + 2) + 3)/(-1(-1|x - 1| + 2) + 2)) + 1) + 1))) - 2 and g(x) = (-2(3(1(-2x^2 + 4x + 1)^2 + 4(-2x^2 + 4x + 1)) - 2) + 2)/(2(3(1(-2x^2 + 4x + 1)^2 + 4(-2x^2 + 4x + 1)) - 2) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(-3cos(3\u03c0((3(1(3x^2 + 2x + 4)) - 1)/(-1(1(3x^2 + 2x + 4)) - 2)) + 1) + 2) + 4 and g(x) = -1(2|((-3(1|x + 2| + 1) + 2)/(-1(1|x + 2| + 1) + 3)) - 1| - 3) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 1(-2((-1(-3|(1x^2 + 1x) + 1| + 3) - 2)/(-2(-3|(1x^2 + 1x) + 1| + 3))) + 4) - 3 and g(x) = -4(-3|((-3(-2x^2 + 4x + 5))/(2(-2x^2 + 4x + 5) - 1)) + 3| - 3) + 4 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (3((1(-1(2|(1|x - 3| + 3) - 2|) + 5) + 1)/(-2(-1(2|(1|x - 3| + 3) - 2|) + 5) - 1)) + 3)/(-2((1(-1(2|(1|x - 3| + 3) - 2|) + 5) + 1)/(-2(-1(2|(1|x - 3| + 3) - 2|) + 5) - 1)) + 3) and g(x) = (1(-1(3e^(1(-4x^2 - 1x - 3)) - 2)^2 + 2(3e^(1(-4x^2 - 1x - 3)) - 2) - 2) - 3)/(-2(-1(3e^(1(-4x^2 - 1x - 3)) - 2)^2 + 2(3e^(1(-4x^2 - 1x - 3)) - 2) - 2) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (2(4(5(3((3x - 1)/(2x + 1))^2 + 4((3x - 1)/(2x + 1)) - 2) - 4)) - 3)/(1(4(5(3((3x - 1)/(2x + 1))^2 + 4((3x - 1)/(2x + 1)) - 2) - 4)) + 2) and g(x) = (2((1((-1((-1x)/(1x - 3)) - 1)/(-2((-1x)/(1x - 3)) + 3)) + 2)/(-3((-1((-1x)/(1x - 3)) - 1)/(-2((-1x)/(1x - 3)) + 3)) + 1)) + 3)/(-2((1((-1((-1x)/(1x - 3)) - 1)/(-2((-1x)/(1x - 3)) + 3)) + 2)/(-3((-1((-1x)/(1x - 3)) - 1)/(-2((-1x)/(1x - 3)) + 3)) + 1)) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (3((1(1(-2((2x + 1)/(3x - 2)) - 3) - 1))/(-3(1(-2((2x + 1)/(3x - 2)) - 3) - 1) + 4)) - 1)/(3((1(1(-2((2x + 1)/(3x - 2)) - 3) - 1))/(-3(1(-2((2x + 1)/(3x - 2)) - 3) - 1) + 4)) + 1) and g(x) = (-3((2(-3((-2x - 3)/(3x - 2))^2 - 1((-2x - 3)/(3x - 2)) - 1) + 3)/(2(-3((-2x - 3)/(3x - 2))^2 - 1((-2x - 3)/(3x - 2)) - 1))) + 2)/(2((2(-3((-2x - 3)/(3x - 2))^2 - 1((-2x - 3)/(3x - 2)) - 1) + 3)/(2(-3((-2x - 3)/(3x - 2))^2 - 1((-2x - 3)/(3x - 2)) - 1))) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1((3((-2(3(1|x - 2| - 3)^2 - 2(1|x - 2| - 3) + 5) + 3)/(-3(3(1|x - 2| - 3)^2 - 2(1|x - 2| - 3) + 5) + 1)) - 2)/(1((-2(3(1|x - 2| - 3)^2 - 2(1|x - 2| - 3) + 5) + 3)/(-3(3(1|x - 2| - 3)^2 - 2(1|x - 2| - 3) + 5) + 1)))) - 1 and g(x) = 1(-1|(3((3x - 2)/(-3x - 2)) - 1) - 3|) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2(3(-5(-2(1x - 5) - 4) + 5)^2 + 4(-5(-2(1x - 5) - 4) + 5) - 5) - 4 and g(x) = 5((-2(3|(5x^2 - 5x - 4) + 3| + 1) + 1)/(-2(3|(5x^2 - 5x - 4) + 3| + 1) - 2))^2 - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3|(-1|((1(-1sin(1\u03c0((1x - 2)/(-2x + 3))) - 3) - 2)/(1(-1sin(1\u03c0((1x - 2)/(-2x + 3))) - 3) + 2)) - 1| + 2) + 3| - 1 and g(x) = 3(2((2(2x + 4) - 1)/(2(2x + 4) + 3)) - 2) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3((-1(-4(-2|(2x^2 + 3x - 1) - 3|) - 4))/(-1(-4(-2|(2x^2 + 3x - 1) - 3|) - 4) + 2)) - 5 and g(x) = -2e^(-1(5(-2|(5x - 5)| + 1))) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (1(-4(-1(-1(2x + 3) + 3)^2 - 5(-1(2x + 3) + 3) + 1) + 1) + 3)/(2(-4(-1(-1(2x + 3) + 3)^2 - 5(-1(2x + 3) + 3) + 1) + 1)) and g(x) = (2((-2((-2(2sin(1\u03c0x)) - 1)/(2(2sin(1\u03c0x)))) + 1)/(2((-2(2sin(1\u03c0x)) - 1)/(2(2sin(1\u03c0x)))))) + 1)/(2((-2((-2(2sin(1\u03c0x)) - 1)/(2(2sin(1\u03c0x)))) + 1)/(2((-2(2sin(1\u03c0x)) - 1)/(2(2sin(1\u03c0x)))))) + 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3e^(2((-2(-5(1((1x)/(1x + 2))^2 - 5)^2 + 4(1((1x)/(1x + 2))^2 - 5) - 5) + 3)/(-1(-5(1((1x)/(1x + 2))^2 - 5)^2 + 4(1((1x)/(1x + 2))^2 - 5) - 5) - 1))) - 3 and g(x) = (1(-2(2|((-1x - 1)/(1x - 3)) + 2| - 2)^2 + 5(2|((-1x - 1)/(1x - 3)) + 2| - 2) - 1) - 3)/(2(-2(2|((-1x - 1)/(1x - 3)) + 2| - 2)^2 + 5(2|((-1x - 1)/(1x - 3)) + 2| - 2) - 1) - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -3(-1(1(-3|((2x)/(3x - 2)) - 3| - 3)^2 - 4(-3|((2x)/(3x - 2)) - 3| - 3) + 1) + 1) - 2 and g(x) = 2e^(-1((2(1((-2x - 2)/(1x - 3)) + 4))/(3(1((-2x - 2)/(1x - 3)) + 4) + 2))) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1((-1(-1|((1(1sin(3\u03c0x - 3)) - 1)/(2(1sin(3\u03c0x - 3)) - 3)) - 1|) - 1)/(3(-1|((1(1sin(3\u03c0x - 3)) - 1)/(2(1sin(3\u03c0x - 3)) - 3)) - 1|) - 2))^2 - 1 and g(x) = -3e^(2((2((-1(5x - 2) + 1)/(1(5x - 2) + 2)) - 1)/(3((-1(5x - 2) + 1)/(1(5x - 2) + 2)) + 2))) + 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2((-1((1(-3|((3x + 1)/(-2x - 3)) - 1| + 2) + 2)/(-2(-3|((3x + 1)/(-2x - 3)) - 1| + 2) - 3)) - 1)/(2((1(-3|((3x + 1)/(-2x - 3)) - 1| + 2) + 2)/(-2(-3|((3x + 1)/(-2x - 3)) - 1| + 2) - 3)) + 3)) - 3)/(2((-1((1(-3|((3x + 1)/(-2x - 3)) - 1| + 2) + 2)/(-2(-3|((3x + 1)/(-2x - 3)) - 1| + 2) - 3)) - 1)/(2((1(-3|((3x + 1)/(-2x - 3)) - 1| + 2) + 2)/(-2(-3|((3x + 1)/(-2x - 3)) - 1| + 2) - 3)) + 3)) + 1) and g(x) = 2|(1|(-3|(-3x + 4) + 3| + 2)| + 3) + 3| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|(-3(1((-1((-1x + 1)/(-2x + 3)) + 2)/(2((-1x + 1)/(-2x + 3)) - 1))^2 - 3((-1((-1x + 1)/(-2x + 3)) + 2)/(2((-1x + 1)/(-2x + 3)) - 1)) + 1) - 5) + 1| - 2 and g(x) = -2|(1(-1|(-4x - 5) - 3| - 1) + 5) - 2| meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2((1(4(1(2x^2 - 1x)^2 - 1(2x^2 - 1x) - 1) - 1) - 1)/(-1(4(1(2x^2 - 1x)^2 - 1(2x^2 - 1x) - 1) - 1) - 1))^2 - 3((1(4(1(2x^2 - 1x)^2 - 1(2x^2 - 1x) - 1) - 1) - 1)/(-1(4(1(2x^2 - 1x)^2 - 1(2x^2 - 1x) - 1) - 1) - 1)) + 3 and g(x) = 1(-2|(-3|(-3|x + 2| - 2)| - 1) - 2|)^2 - 4(-2|(-3|(-3|x + 2| - 2)| - 1) - 2|) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3(3|((-2(-3|(-4x - 3) + 1| - 3) + 3)/(-1(-3|(-4x - 3) + 1| - 3) - 2)) + 2| + 2) - 1 and g(x) = 2e^(-2(-5(2|((-2x - 2)/(3x)) + 3| - 1) - 1)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 3(2|(1|(1(2x + 2)^2 - 3(2x + 2) - 3) + 2|)| - 2) + 3 and g(x) = 1((3(-1|(-3e^(-1x) + 1) + 3| + 1))/(-3(-1|(-3e^(-1x) + 1) + 3| + 1) - 3)) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -4(4(3|(-2e^(-2(-4x^2 + 5x + 3)) - 1) + 2| - 2) + 2)^2 + 3(4(3|(-2e^(-2(-4x^2 + 5x + 3)) - 1) + 2| - 2) + 2) + 4 and g(x) = 1((-2(-1|(2x - 5)| - 2) + 3)/(1(-1|(2x - 5)| - 2)))^2 - 1((-2(-1|(2x - 5)| - 2) + 3)/(1(-1|(2x - 5)| - 2))) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1e^(2(-5(-1|(1(5x^2 + 3x - 1)^2 + 2(5x^2 + 3x - 1) + 4) + 2| - 2)^2 - 5(-1|(1(5x^2 + 3x - 1)^2 + 2(5x^2 + 3x - 1) + 4) + 2| - 2) - 3)) and g(x) = 5(-5(1((-2x)/(-1x + 2)))^2 + 3(1((-2x)/(-1x + 2))) + 4) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1|(-3(-3|(-1(-3x - 5)^2 - 4(-3x - 5)) - 1| - 3) - 1) - 2| + 1 and g(x) = -2(-3((-2(-2x - 1) - 2)/(-1(-2x - 1) + 2))^2 + 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-1((1(-1((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3))^2 + 3((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3)) + 3) + 2)/(-3(-1((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3))^2 + 3((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3)) + 3) + 4)) - 2)/(-3((1(-1((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3))^2 + 3((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3)) + 3) + 2)/(-3(-1((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3))^2 + 3((2((-2x)/(-2x - 1)) - 3)/(-1((-2x)/(-2x - 1)) - 3)) + 3) + 4)) - 3) and g(x) = -2cos(3\u03c0(5((-1((-1x - 2)/(2x - 1)) - 1)/(2((-1x - 2)/(2x - 1)) + 3)) - 1) + 1) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (3(-2|(-2(2(1|x - 2| + 2) - 1) - 5)| - 3))/(1(-2|(-2(2(1|x - 2| + 2) - 1) - 5)| - 3) + 3) and g(x) = 3|((1((2(2e^(2x) - 3) - 3)/(-1(2e^(2x) - 3) + 2)) + 2)/(3((2(2e^(2x) - 3) - 3)/(-1(2e^(2x) - 3) + 2)) + 2)) + 1| in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 4(-3cos(3\u03c0((1(-5(2|x - 1| - 1)^2 - 4(2|x - 1| - 1) - 2) + 3)/(1(-5(2|x - 1| - 1)^2 - 4(2|x - 1| - 1) - 2))) + 1) + 3)^2 - 3(-3cos(3\u03c0((1(-5(2|x - 1| - 1)^2 - 4(2|x - 1| - 1) - 2) + 3)/(1(-5(2|x - 1| - 1)^2 - 4(2|x - 1| - 1) - 2))) + 1) + 3) - 1 and g(x) = -1|(1(-3(2e^(-1x) - 1) + 5) - 4) + 3| + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(-1(1(2(5x - 2) - 1) - 5) - 2) + 2)/(3(-1(1(2(5x - 2) - 1) - 5) - 2) - 2) and g(x) = 1((-1(-3|(-1sin(3\u03c0x + 3) - 2) - 1|))/(2(-3|(-1sin(3\u03c0x + 3) - 2) - 1|)))^2 + 1((-1(-3|(-1sin(3\u03c0x + 3) - 2) - 1|))/(2(-3|(-1sin(3\u03c0x + 3) - 2) - 1|))) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2(-3(-1((-2((-2x + 3)/(1x + 2)) - 3)/(1((-2x + 3)/(1x + 2)))) - 5) + 4) + 5 and g(x) = -2|(-2sin(2\u03c0(-1|(-4x + 3) + 1| + 1) + 2) - 3) + 1| - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1(-3|(3|(-2(1e^(2x) + 1)^2 - 4(1e^(2x) + 1) + 5) + 3| - 2) + 2| - 2) + 3)/(3(-3|(3|(-2(1e^(2x) + 1)^2 - 4(1e^(2x) + 1) + 5) + 3| - 2) + 2| - 2) - 2) and g(x) = -1(3(1|(-1e^(-1x) + 2)| - 3) - 1)^2 + 1(3(1|(-1e^(-1x) + 2)| - 3) - 1) + 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(-3(-4(1(-5x^2 + 4x + 2))^2 - 5(1(-5x^2 + 4x + 2)))^2 + 1(-4(1(-5x^2 + 4x + 2))^2 - 5(1(-5x^2 + 4x + 2)))) - 3)/(2(-3(-4(1(-5x^2 + 4x + 2))^2 - 5(1(-5x^2 + 4x + 2)))^2 + 1(-4(1(-5x^2 + 4x + 2))^2 - 5(1(-5x^2 + 4x + 2)))) - 1) and g(x) = -1(1(2e^(-1(-2|x + 2| + 3)))) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(1|(-3|(-4(-1cos(2\u03c0x + 2) + 2) + 1)|) - 1| + 3) + 2| + 1 and g(x) = 5(1((3(4x - 5) + 2)/(-2(4x - 5) + 3)) + 2) + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3(-3(5(-3(-2|x + 1| - 3) - 5)^2 - 5(-3(-2|x + 1| - 3) - 5) + 4)^2 + 3(5(-3(-2|x + 1| - 3) - 5)^2 - 5(-3(-2|x + 1| - 3) - 5) + 4) - 3))/(3(-3(5(-3(-2|x + 1| - 3) - 5)^2 - 5(-3(-2|x + 1| - 3) - 5) + 4)^2 + 3(5(-3(-2|x + 1| - 3) - 5)^2 - 5(-3(-2|x + 1| - 3) - 5) + 4) - 3)) and g(x) = 1(-1|(-4((2x - 2)/(-1x - 1)) + 3) - 2| - 2)^2 + 4(-1|(-4((2x - 2)/(-1x - 1)) + 3) - 2| - 2) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(4((-2(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 1)/(3(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 3))^2 - 1((-2(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 1)/(3(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 3)) - 3) - 2)/(2(4((-2(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 1)/(3(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 3))^2 - 1((-2(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 1)/(3(-2(-2x^2 - 1x - 3)^2 + 5(-2x^2 - 1x - 3) - 1) + 3)) - 3)) and g(x) = -3(-1((2(-1x + 4) - 2)/(1(-1x + 4))) + 2) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1|(-1e^(1(-1((-3(-4x + 2) + 3)/(3(-4x + 2))) - 1)) - 3) - 3| - 1 and g(x) = -5(-4((-3(2x^2 + 2x + 5) + 3)/(-1(2x^2 + 2x + 5) + 2))^2 - 5((-3(2x^2 + 2x + 5) + 3)/(-1(2x^2 + 2x + 5) + 2)) - 2) - 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3((-3(2cos(1\u03c0(3|((-2x + 2)/(3x - 1)) - 1| - 3) - 1) + 3) - 3)/(-3(2cos(1\u03c0(3|((-2x + 2)/(3x - 1)) - 1| - 3) - 1) + 3) - 1)) - 1)/(-1((-3(2cos(1\u03c0(3|((-2x + 2)/(3x - 1)) - 1| - 3) - 1) + 3) - 3)/(-3(2cos(1\u03c0(3|((-2x + 2)/(3x - 1)) - 1| - 3) - 1) + 3) - 1)) + 2) and g(x) = 1((3(-4(-2|x - 1|)^2 - 3(-2|x - 1|)) - 2)/(3(-4(-2|x - 1|)^2 - 3(-2|x - 1|)) + 1)) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1(-2e^(2(-4(-2((-3x - 3)/(1x))^2 - 4((-3x - 3)/(1x)) + 3) - 1)) + 2) + 1 and g(x) = -2|((-1(1((-1x - 2)/(3x - 2)) + 4) + 2)/(-3(1((-1x - 2)/(3x - 2)) + 4) - 3)) - 1| + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-2(-5(1(-3|(4x^2 + 1x + 2) - 3|) + 2) - 2))/(-2(-5(1(-3|(4x^2 + 1x + 2) - 3|) + 2) - 2) + 3) and g(x) = 3|(1|(3|(-5x + 3) + 1| - 3) - 3| - 1) + 1| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1|(4((3(5(-4x^2 + 3x + 1) - 1) + 1)/(2(5(-4x^2 + 3x + 1) - 1) + 1)) + 3) + 2| and g(x) = -1|(3(-1(-1x + 5)^2 - 4(-1x + 5) - 2) - 1) - 1| meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -3(-3|(5(-2cos(1\u03c0(-2x + 5) + 3) + 1)^2 - 5(-2cos(1\u03c0(-2x + 5) + 3) + 1) - 2) - 2| - 3)^2 + 5(-3|(5(-2cos(1\u03c0(-2x + 5) + 3) + 1)^2 - 5(-2cos(1\u03c0(-2x + 5) + 3) + 1) - 2) - 2| - 3) + 3 and g(x) = (1((3(-1|(-5x - 1) + 3| + 2) + 3)/(3(-1|(-5x - 1) + 3| + 2) - 1)) + 2)/(-3((3(-1|(-5x - 1) + 3| + 2) + 3)/(3(-1|(-5x - 1) + 3| + 2) - 1)) + 1) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-3((2(1((-2(-3|x - 1| - 3) - 2)/(-1(-3|x - 1| - 3) + 2)) - 4))/(-1(1((-2(-3|x - 1| - 3) - 2)/(-1(-3|x - 1| - 3) + 2)) - 4) - 2)) - 1)/(1((2(1((-2(-3|x - 1| - 3) - 2)/(-1(-3|x - 1| - 3) + 2)) - 4))/(-1(1((-2(-3|x - 1| - 3) - 2)/(-1(-3|x - 1| - 3) + 2)) - 4) - 2)) + 3) and g(x) = 4(1|((-1((1x + 1)/(-3x - 2)) - 3)/(-1((1x + 1)/(-3x - 2)) - 2)) + 3| - 3) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-2(2(2((1((-1x - 3)/(-1x + 2)) - 3)/(-1((-1x - 3)/(-1x + 2)) + 2))^2 + 4((1((-1x - 3)/(-1x + 2)) - 3)/(-1((-1x - 3)/(-1x + 2)) + 2)) - 2) + 1) + 1)/(3(2(2((1((-1x - 3)/(-1x + 2)) - 3)/(-1((-1x - 3)/(-1x + 2)) + 2))^2 + 4((1((-1x - 3)/(-1x + 2)) - 3)/(-1((-1x - 3)/(-1x + 2)) + 2)) - 2) + 1) + 3) and g(x) = -1|((2(-1e^(-1(4x^2 - 1x - 1)) - 3) + 1)/(-2(-1e^(-1(4x^2 - 1x - 1)) - 3) + 1)) + 2| intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3(-2|(-5(-3|(2sin(1\u03c0x - 2) + 3) - 3|)^2 - 3(-3|(2sin(1\u03c0x - 2) + 3) - 3|) - 4) - 1| + 3) + 1 and g(x) = (1((-1(2|(2|x - 1| - 2) + 1| - 3) + 3)/(-1(2|(2|x - 1| - 2) + 1| - 3) + 2)) + 1)/(-3((-1(2|(2|x - 1| - 2) + 1| - 3) + 3)/(-1(2|(2|x - 1| - 2) + 1| - 3) + 2)) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3cos(2\u03c0(-4(3(1(-1|x + 2| + 1)^2 + 2(-1|x + 2| + 1) + 5) + 5)) - 3) + 2 and g(x) = 5(1(-3((2x + 2)/(-3x - 2)) + 4) - 2)^2 - 2(1(-3((2x + 2)/(-3x - 2)) + 4) - 2) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2(-4((3((2(1x + 1))/(-1(1x + 1) - 1)) + 1)/(-1((2(1x + 1))/(-1(1x + 1) - 1)) + 2)) + 4) - 3 and g(x) = 1((1(-4(2x^2 - 1x + 5) + 3) - 2)/(-3(-4(2x^2 - 1x + 5) + 3) + 4))^2 + 5((1(-4(2x^2 - 1x + 5) + 3) - 2)/(-3(-4(2x^2 - 1x + 5) + 3) + 4)) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5(1((1((1(-3x^2 - 5x - 2) + 1)/(-2(-3x^2 - 5x - 2) - 3)) - 1)/(-1((1(-3x^2 - 5x - 2) + 1)/(-2(-3x^2 - 5x - 2) - 3)) - 3)) + 3) + 4 and g(x) = 3|((-1((-2(5x + 2) + 2)/(2(5x + 2) - 1)) + 2)/(-3((-2(5x + 2) + 2)/(2(5x + 2) - 1)) + 1)) + 3| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -4(-2(-2|((-2(2|x + 2| - 2) - 1)/(-1(2|x + 2| - 2) - 3)) + 2| + 3) + 1) - 2 and g(x) = (2(-1e^(1((-3(-3x))/(1(-3x) + 2))) + 2) + 2)/(-2(-1e^(1((-3(-3x))/(1(-3x) + 2))) + 2) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (2(3(3e^(-2(4(1x^2 - 5x - 3) + 5)))^2 - 4(3e^(-2(4(1x^2 - 5x - 3) + 5)))) + 2)/(-1(3(3e^(-2(4(1x^2 - 5x - 3) + 5)))^2 - 4(3e^(-2(4(1x^2 - 5x - 3) + 5))))) and g(x) = 3(-1((-3(5x^2 - 4x + 1) + 3)/(-2(5x^2 - 4x + 1) + 1))^2 - 1((-3(5x^2 - 4x + 1) + 3)/(-2(5x^2 - 4x + 1) + 1)) + 4)^2 + 3(-1((-3(5x^2 - 4x + 1) + 3)/(-2(5x^2 - 4x + 1) + 1))^2 - 1((-3(5x^2 - 4x + 1) + 3)/(-2(5x^2 - 4x + 1) + 1)) + 4) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (3((2((2((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)) + 2)/(-3((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)))))/(3((2((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)) + 2)/(-3((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)))) - 2)) - 1)/(-1((2((2((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)) + 2)/(-3((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)))))/(3((2((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)) + 2)/(-3((-1(-2e^(-1x) + 3) - 1)/(-3(-2e^(-1x) + 3) - 1)))) - 2)) - 1) and g(x) = (1(-3(4(4x - 1) - 5) - 3) - 1)/(-3(-3(4(4x - 1) - 5) - 3) - 2) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2|((-1(-3(2|(2x + 2) + 1| - 2)^2 - 3(2|(2x + 2) + 1| - 2) + 4) + 3)/(1(-3(2|(2x + 2) + 1| - 2)^2 - 3(2|(2x + 2) + 1| - 2) + 4) + 2)) + 3| + 3 and g(x) = 3|(-1e^(-1(3((-1x - 1)/(2x + 1)) + 1)) + 1) - 1| - 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 3((-1(3|(-1((-1x + 1)/(1x + 2)) - 1) - 1| - 2) - 1)/(2(3|(-1((-1x + 1)/(1x + 2)) - 1) - 1| - 2) + 1)) - 1 and g(x) = 1|((-2(2(-5x^2 + 3) + 2) - 2)/(-3(2(-5x^2 + 3) + 2) + 4)) + 3| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1|(3(-1|((-1(-1|x - 3| + 2) + 3)/(-2(-1|x - 3| + 2) + 1)) - 1| - 2) - 4) + 1| + 1 and g(x) = 2((2(1((-2x + 3)/(3x - 2)) + 2) - 2)/(-2(1((-2x + 3)/(3x - 2)) + 2) - 1)) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2|(3|((-1(-1((2x + 3)/(1x)) - 1) + 3)/(3(-1((2x + 3)/(1x)) - 1))) - 1|) + 3| + 2 and g(x) = -4((-2(-5(1x + 5) + 3) - 3)/(-2(-5(1x + 5) + 3))) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4(-3e^(1(4(-2((1x)/(2x - 1)) - 2)^2 - 3(-2((1x)/(2x - 1)) - 2) - 3)) + 2) and g(x) = -1|(-3(-1|(3sin(2\u03c0x) + 2) - 3| - 1)^2 - 4(-1|(3sin(2\u03c0x) + 2) - 3| - 1) - 1) + 2| + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(-2|((-2(-1(5x^2 + 3x - 4)) - 2)/(3(-1(5x^2 + 3x - 4)))) - 3|) and g(x) = -1cos(1\u03c0((1((1(5x^2 + 5x) + 1)/(1(5x^2 + 5x) + 2)) + 1)/(-1((1(5x^2 + 5x) + 1)/(1(5x^2 + 5x) + 2)) - 1))) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-2(-3((1(-3cos(2\u03c0(1x^2 - 1x - 3)) + 2) + 3)/(-2(-3cos(2\u03c0(1x^2 - 1x - 3)) + 2)))^2 + 5((1(-3cos(2\u03c0(1x^2 - 1x - 3)) + 2) + 3)/(-2(-3cos(2\u03c0(1x^2 - 1x - 3)) + 2)))))/(2(-3((1(-3cos(2\u03c0(1x^2 - 1x - 3)) + 2) + 3)/(-2(-3cos(2\u03c0(1x^2 - 1x - 3)) + 2)))^2 + 5((1(-3cos(2\u03c0(1x^2 - 1x - 3)) + 2) + 3)/(-2(-3cos(2\u03c0(1x^2 - 1x - 3)) + 2))))) and g(x) = -2((2(5(1x)^2 + 1(1x) - 3) + 1)/(-2(5(1x)^2 + 1(1x) - 3) - 2)) - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3|(1|(-2|(3|(-3x) - 2| + 1) - 2| + 1) + 2| + 3) + 2| and g(x) = 1|(2(-4(-1|x - 1| - 1) + 3) + 2) - 2| - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(3cos(1\u03c0((2(3(3x - 5) + 1) + 3)/(-1(3(3x - 5) + 1) + 2)) + 3) - 2) - 3)/(3(3cos(1\u03c0((2(3(3x - 5) + 1) + 3)/(-1(3(3x - 5) + 1) + 2)) + 3) - 2) + 3) and g(x) = -3|(2|(-3|((2x + 2)/(1x - 3)) - 2| + 3) + 2|) + 3| - 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2|(-3(-3|((-2(1|x - 3| - 1) + 1)/(-3(1|x - 3| - 1) - 1)) + 2| + 3))| + 2 and g(x) = 4(-2((1((1x + 3)/(-2x)) + 3)/(2((1x + 3)/(-2x)) + 3)) - 4) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1(1((2(1|(1|x + 3| - 1) - 2| - 2) - 2)/(2(1|(1|x + 3| - 1) - 2| - 2) + 2)) - 4) + 3 and g(x) = (-2(5(-4((2x)/(2x + 3)) - 2)^2 + 5(-4((2x)/(2x + 3)) - 2) + 2) + 3)/(2(5(-4((2x)/(2x + 3)) - 2)^2 + 5(-4((2x)/(2x + 3)) - 2) + 2) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(1((2(3|(-1e^(-1x) - 3) + 3|))/(-1(3|(-1e^(-1x) - 3) + 3|) + 2)) + 4))/(-3(1((2(3|(-1e^(-1x) - 3) + 3|))/(-1(3|(-1e^(-1x) - 3) + 3|) + 2)) + 4) + 1) and g(x) = (1(4(-1(1x^2 + 3x)^2 + 2(1x^2 + 3x) + 3)^2 + 1(-1(1x^2 + 3x)^2 + 2(1x^2 + 3x) + 3) + 2) - 2)/(-1(4(-1(1x^2 + 3x)^2 + 2(1x^2 + 3x) + 3)^2 + 1(-1(1x^2 + 3x)^2 + 2(1x^2 + 3x) + 3) + 2) - 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2((2(-3|(2cos(3\u03c0((-3x - 3)/(-2x + 3)) - 1) - 3) - 1| - 2) + 1)/(-1(-3|(2cos(3\u03c0((-3x - 3)/(-2x + 3)) - 1) - 3) - 1| - 2) - 3)) + 1 and g(x) = 2(-4((-3(-1x) + 3)/(1(-1x) + 1)) + 2) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (2(-3|(2sin(2\u03c0(4(-1x^2) - 2))) - 2| + 2) + 1)/(2(-3|(2sin(2\u03c0(4(-1x^2) - 2))) - 2| + 2) + 1) and g(x) = -1((-3((-2(-1|x + 2|) - 1)/(-3(-1|x + 2|) - 3)) + 3)/(3((-2(-1|x + 2|) - 1)/(-3(-1|x + 2|) - 3)) + 3)) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -4(-4((-3((-1((-3x + 2)/(-1x + 2)))/(2((-3x + 2)/(-1x + 2)) + 3)) - 1)/(3((-1((-3x + 2)/(-1x + 2)))/(2((-3x + 2)/(-1x + 2)) + 3)))) - 3) + 4 and g(x) = 5(3|(-1(1e^(2x) + 2) + 4) + 3| + 3)^2 - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3(1(-3(-1(-1|x - 2| - 2) + 1)^2 - 1(-1(-1|x - 2| - 2) + 1)) - 4)^2 - 4 and g(x) = 1|(-3((-2((-2x - 3)/(-1x - 1)) + 2)/(-3((-2x - 3)/(-1x - 1)) + 4))^2 + 3((-2((-2x - 3)/(-1x - 1)) + 2)/(-3((-2x - 3)/(-1x - 1)) + 4)) + 4) - 3| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (2(-5(2(-1|(-3e^(1x) + 2) + 1| + 3)^2 + 3(-1|(-3e^(1x) + 2) + 1| + 3) - 3) - 4) + 1)/(-3(-5(2(-1|(-3e^(1x) + 2) + 1| + 3)^2 + 3(-1|(-3e^(1x) + 2) + 1| + 3) - 3) - 4) + 2) and g(x) = -1|(-2(-3((-2x + 2)/(-3x + 2)) - 2)^2 - 2(-3((-2x + 2)/(-3x + 2)) - 2) - 3)| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2(-2(-1(2(2|x + 2| + 1)^2 - 1(2|x + 2| + 1)) + 4) - 5) + 1 and g(x) = 3(-2|(-4(-4x + 4)^2 - 3(-4x + 4) - 5) - 2| + 2) - 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1|(-3((3((-3((-2x + 3)/(-3x + 4)) + 1)/(-3((-2x + 3)/(-3x + 4)) - 1)))/(-3((-3((-2x + 3)/(-3x + 4)) + 1)/(-3((-2x + 3)/(-3x + 4)) - 1)) + 1)) + 4) + 3| - 2 and g(x) = (1(1|(-4(-1x^2 - 1x + 4)^2 + 1(-1x^2 - 1x + 4) - 5) - 2| - 2) + 1)/(3(1|(-4(-1x^2 - 1x + 4)^2 + 1(-1x^2 - 1x + 4) - 5) - 2| - 2) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(-3|((1(3cos(3\u03c0(1|x - 1| + 1) - 1) - 2) + 3)/(1(3cos(3\u03c0(1|x - 1| + 1) - 1) - 2) + 3)) + 2| - 2) - 3| - 1 and g(x) = -1|(5(-1(2e^(2x) + 2)^2 + 3(2e^(2x) + 2) - 1) - 3) - 1| - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3((2(2|(4(-3x^2 + 3)^2 - 2(-3x^2 + 3) + 2) + 3| + 3) + 1)/(-1(2|(4(-3x^2 + 3)^2 - 2(-3x^2 + 3) + 2) + 3| + 3) + 2)) - 5 and g(x) = (1((3(-1|(-1|x + 3| + 2) + 3| + 2) - 1)/(3(-1|(-1|x + 3| + 2) + 3| + 2))) + 2)/(-2((3(-1|(-1|x + 3| + 2) + 3| + 2) - 1)/(3(-1|(-1|x + 3| + 2) + 3| + 2))) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -4(-2|((3(-3(-2sin(1\u03c0x + 1) - 2) + 3) + 3)/(-3(-3(-2sin(1\u03c0x + 1) - 2) + 3) + 2)) + 2| + 3)^2 - 3(-2|((3(-3(-2sin(1\u03c0x + 1) - 2) + 3) + 3)/(-3(-3(-2sin(1\u03c0x + 1) - 2) + 3) + 2)) + 2| + 3) - 2 and g(x) = -1e^(1((-3(1(4x^2 - 4x - 5) - 5) + 1)/(-2(1(4x^2 - 4x - 5) - 5)))) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1(1(-2|(5(3x - 4) + 2) - 3| - 2)^2 + 2(-2|(5(3x - 4) + 2) - 3| - 2))^2 + 3 and g(x) = 5(-4((-3(-3x + 4) - 1)/(-2(-3x + 4) + 1)) + 3) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-1((-3((-2(-3((3x - 3)/(-1x - 3)) - 5))/(-3(-3((3x - 3)/(-1x - 3)) - 5))) - 1)/(1((-2(-3((3x - 3)/(-1x - 3)) - 5))/(-3(-3((3x - 3)/(-1x - 3)) - 5))) - 2)) + 1)/(1((-3((-2(-3((3x - 3)/(-1x - 3)) - 5))/(-3(-3((3x - 3)/(-1x - 3)) - 5))) - 1)/(1((-2(-3((3x - 3)/(-1x - 3)) - 5))/(-3(-3((3x - 3)/(-1x - 3)) - 5))) - 2)) - 3) and g(x) = -2e^(-1(1(4(1x + 1) - 5) - 2)) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3|(-4(5((-3(-1x^2 - 4x - 4))/(1(-1x^2 - 4x - 4))) + 2)^2 - 1(5((-3(-1x^2 - 4x - 4))/(1(-1x^2 - 4x - 4))) + 2) - 5) - 2| + 2 and g(x) = -2(-5(5((3x + 2)/(1x + 3))^2 - 1((3x + 2)/(1x + 3)) + 4))^2 + 5(-5(5((3x + 2)/(1x + 3))^2 - 1((3x + 2)/(1x + 3)) + 4)) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 1((2(3|(1(-2|x + 3| - 1)^2 + 1(-2|x + 3| - 1) + 5) + 1| + 3) + 3)/(1(3|(1(-2|x + 3| - 1)^2 + 1(-2|x + 3| - 1) + 5) + 1| + 3) + 1))^2 + 1((2(3|(1(-2|x + 3| - 1)^2 + 1(-2|x + 3| - 1) + 5) + 1| + 3) + 3)/(1(3|(1(-2|x + 3| - 1)^2 + 1(-2|x + 3| - 1) + 5) + 1| + 3) + 1)) + 2 and g(x) = 2(1(3|((-1x - 2)/(-3x + 4)) + 1| - 1))^2 + 2(1(3|((-1x - 2)/(-3x + 4)) + 1| - 1)) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2e^(1((-2(1|(3|((2x + 1)/(-2x - 2)) + 3| - 2) - 1| - 1) + 3)/(-1(1|(3|((2x + 1)/(-2x - 2)) + 3| - 2) - 1| - 1)))) + 3 and g(x) = 2(-1|((-2((-3x - 2)/(2x - 3)) - 3)/(-2((-3x - 2)/(2x - 3)) + 1)) + 2| + 2)^2 - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-2((2(-1|(-1|((3x + 2)/(-2x - 1)) - 1| - 2) + 2| - 3) + 1)/(2(-1|(-1|((3x + 2)/(-2x - 1)) - 1| - 2) + 2| - 3) + 3)) + 1)/(-1((2(-1|(-1|((3x + 2)/(-2x - 1)) - 1| - 2) + 2| - 3) + 1)/(2(-1|(-1|((3x + 2)/(-2x - 1)) - 1| - 2) + 2| - 3) + 3)) - 1) and g(x) = (2(2|(2|((2x)/(-1x - 1)) + 1| - 1)| - 1) - 2)/(3(2|(2|((2x)/(-1x - 1)) + 1| - 1)| - 1) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1(3(3e^(-1(-5((-1x + 2)/(2x - 1))^2 + 1((-1x + 2)/(2x - 1)) + 4)) - 1)^2 + 3(3e^(-1(-5((-1x + 2)/(2x - 1))^2 + 1((-1x + 2)/(2x - 1)) + 4)) - 1) - 3) + 4 and g(x) = (2(3(2cos(3\u03c0(-3|x - 3| + 3) + 2) - 3)^2 - 4(2cos(3\u03c0(-3|x - 3| + 3) + 2) - 3) + 1) + 1)/(-1(3(2cos(3\u03c0(-3|x - 3| + 3) + 2) - 3)^2 - 4(2cos(3\u03c0(-3|x - 3| + 3) + 2) - 3) + 1) + 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(5(-4(-1|(-1x) - 3|)^2 - 1(-1|(-1x) - 3|) + 2) - 3)^2 + 1(5(-4(-1|(-1x) - 3|)^2 - 1(-1|(-1x) - 3|) + 2) - 3) - 2 and g(x) = -2((1(3(-2sin(2\u03c0x - 2) - 2)^2 + 5(-2sin(2\u03c0x - 2) - 2) - 2))/(-2(3(-2sin(2\u03c0x - 2) - 2)^2 + 5(-2sin(2\u03c0x - 2) - 2) - 2) + 1))^2 - 2((1(3(-2sin(2\u03c0x - 2) - 2)^2 + 5(-2sin(2\u03c0x - 2) - 2) - 2))/(-2(3(-2sin(2\u03c0x - 2) - 2)^2 + 5(-2sin(2\u03c0x - 2) - 2) - 2) + 1)) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-1(-5(2(-1((-1x + 1)/(-3x - 1)) + 2) - 1) + 1))/(1(-5(2(-1((-1x + 1)/(-3x - 1)) + 2) - 1) + 1)) and g(x) = -5(-5(-2|(-2|x + 2| + 1) - 2| + 3) + 4) + 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(-5((3((-2(5x - 3))/(-1(5x - 3) + 3)) + 1)/(-1((-2(5x - 3))/(-1(5x - 3) + 3)) + 3)) - 5) + 3)/(-2(-5((3((-2(5x - 3))/(-1(5x - 3) + 3)) + 1)/(-1((-2(5x - 3))/(-1(5x - 3) + 3)) + 3)) - 5) - 3) and g(x) = 1|(4((3((3x + 2)/(-2x - 1)) + 2)/(2((3x + 2)/(-2x - 1)) + 2)) - 1) + 3| intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2(1(1(-2(2|x - 1| + 1)^2 - 2(2|x - 1| + 1) - 3)^2 - 4(-2(2|x - 1| + 1)^2 - 2(2|x - 1| + 1) - 3) - 1)^2 - 2(1(-2(2|x - 1| + 1)^2 - 2(2|x - 1| + 1) - 3)^2 - 4(-2(2|x - 1| + 1)^2 - 2(2|x - 1| + 1) - 3) - 1) - 5) - 2)/(2(1(1(-2(2|x - 1| + 1)^2 - 2(2|x - 1| + 1) - 3)^2 - 4(-2(2|x - 1| + 1)^2 - 2(2|x - 1| + 1) - 3) - 1)^2 - 2(1(-2(2|x - 1| + 1)^2 - 2(2|x - 1| + 1) - 3)^2 - 4(-2(2|x - 1| + 1)^2 - 2(2|x - 1| + 1) - 3) - 1) - 5) + 3) and g(x) = -3|(-3((2((-3x + 1)/(2x + 2)) - 3)/(1((-3x + 1)/(2x + 2)) - 2)) - 4) + 1| + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1(2(-3(2|(-2|x + 1| + 3) + 1| + 2)^2 + 1(2|(-2|x + 1| + 3) + 1| + 2) + 3) - 1)^2 + 5(2(-3(2|(-2|x + 1| + 3) + 1| + 2)^2 + 1(2|(-2|x + 1| + 3) + 1| + 2) + 3) - 1) + 5 and g(x) = 3(5(-3(-2x + 5) + 5) - 5) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -3(4(-2|(1(-2x^2 - 4x - 3)^2 + 2(-2x^2 - 4x - 3) + 2) + 3| + 3) - 3)^2 + 2(4(-2|(1(-2x^2 - 4x - 3)^2 + 2(-2x^2 - 4x - 3) + 2) + 3| + 3) - 3) + 5 and g(x) = -1(3(4((2x + 1)/(1x + 1))^2 + 2((2x + 1)/(1x + 1)) + 5) + 1) + 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1sin(2\u03c0(-1(-1|(-1(-4x + 2)^2 - 2(-4x + 2) - 5) + 2| + 3)^2 - 3(-1|(-1(-4x + 2)^2 - 2(-4x + 2) - 5) + 2| + 3) - 2) - 3) - 2 and g(x) = (-2(-2(-1(-1e^(-1x)) - 2)^2 - 3(-1(-1e^(-1x)) - 2) + 3) + 1)/(3(-2(-1(-1e^(-1x)) - 2)^2 - 3(-1(-1e^(-1x)) - 2) + 3) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -4(1(-2(-3sin(1\u03c0(-2x - 2) - 3) - 2) - 1)^2 + 2(-2(-3sin(1\u03c0(-2x - 2) - 3) - 2) - 1) + 2) - 4 and g(x) = (-2(1(2(2x^2 + 1x - 3)^2 + 4(2x^2 + 1x - 3) + 4)^2 - 2(2(2x^2 + 1x - 3)^2 + 4(2x^2 + 1x - 3) + 4) - 5) - 1)/(2(1(2(2x^2 + 1x - 3)^2 + 4(2x^2 + 1x - 3) + 4)^2 - 2(2(2x^2 + 1x - 3)^2 + 4(2x^2 + 1x - 3) + 4) - 5) - 1) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1(5((-2(4((-1x + 3)/(2x + 2)) + 1))/(-2(4((-1x + 3)/(2x + 2)) + 1)))^2 - 3((-2(4((-1x + 3)/(2x + 2)) + 1))/(-2(4((-1x + 3)/(2x + 2)) + 1))) + 5)^2 - 3(5((-2(4((-1x + 3)/(2x + 2)) + 1))/(-2(4((-1x + 3)/(2x + 2)) + 1)))^2 - 3((-2(4((-1x + 3)/(2x + 2)) + 1))/(-2(4((-1x + 3)/(2x + 2)) + 1))) + 5) + 4 and g(x) = 2|((1(5(1x^2 - 4x) - 1) + 1)/(-3(5(1x^2 - 4x) - 1) + 2)) - 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2(1|(2cos(1\u03c0(4((1x - 3)/(3x)) + 4) + 1) - 3) - 3| + 1)^2 - 1(1|(2cos(1\u03c0(4((1x - 3)/(3x)) + 4) + 1) - 3) - 3| + 1) + 5 and g(x) = 4((-1((3(5x + 4) + 1)/(-1(5x + 4))) - 3)/(1((3(5x + 4) + 1)/(-1(5x + 4))) - 2))^2 + 3((-1((3(5x + 4) + 1)/(-1(5x + 4))) - 3)/(1((3(5x + 4) + 1)/(-1(5x + 4))) - 2)) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1(5((1((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 1)) + 1)/(1((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 1)) - 2))^2 - 5((1((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 1)) + 1)/(1((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 1)) - 2))) + 2)/(3(5((1((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 1)) + 1)/(1((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 1)) - 2))^2 - 5((1((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 1)) + 1)/(1((3(-1e^(2x) - 3) - 2)/(-3(-1e^(2x) - 3) + 1)) - 2))) + 1) and g(x) = -2((-1(-2e^(1((1x - 1)/(-1x - 3))) + 3) - 3)/(-3(-2e^(1((1x - 1)/(-1x - 3))) + 3) - 3)) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1sin(3\u03c0((1((-1(-2(-4x - 5) - 1) - 1)/(-1(-2(-4x - 5) - 1) - 2)) + 1)/(-3((-1(-2(-4x - 5) - 1) - 1)/(-1(-2(-4x - 5) - 1) - 2)))) - 1) and g(x) = 4((-3(-3(-5x + 1) - 3) - 1)/(-1(-3(-5x + 1) - 3) + 2)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|(-1((-1(4(-3cos(2\u03c0x - 3) - 1)^2 + 3(-3cos(2\u03c0x - 3) - 1) - 1) - 1)/(3(4(-3cos(2\u03c0x - 3) - 1)^2 + 3(-3cos(2\u03c0x - 3) - 1) - 1) - 2)) - 2) - 3| + 3 and g(x) = (3(1|(2e^(-2((-3x - 2)/(2x - 1))) - 2) - 1| - 1))/(3(1|(2e^(-2((-3x - 2)/(2x - 1))) - 2) - 1| - 1) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-3(2|(-1(2(-2x^2 + 1x - 1)^2 + 2(-2x^2 + 1x - 1) - 5)^2 - 4(2(-2x^2 + 1x - 1)^2 + 2(-2x^2 + 1x - 1) - 5) - 2) + 3| + 1) + 1)/(-3(2|(-1(2(-2x^2 + 1x - 1)^2 + 2(-2x^2 + 1x - 1) - 5)^2 - 4(2(-2x^2 + 1x - 1)^2 + 2(-2x^2 + 1x - 1) - 5) - 2) + 3| + 1) - 1) and g(x) = -1(-1e^(-1(1(3x - 3) - 3)) - 3) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 5(3sin(1\u03c0(-1|(3|((3x - 1)/(1x + 2)) + 1| - 2) + 1| + 1) - 3)) - 1 and g(x) = 3(3(2(5x + 4) - 2)^2 + 3(2(5x + 4) - 2) - 4)^2 - 3(3(2(5x + 4) - 2)^2 + 3(2(5x + 4) - 2) - 4) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 5(2(3(4((1x - 3)/(3x))^2 + 5((1x - 3)/(3x)) + 1))^2 - 1(3(4((1x - 3)/(3x))^2 + 5((1x - 3)/(3x)) + 1)) + 1) + 2 and g(x) = -3((3(-4(-3cos(2\u03c0x + 1) + 2)^2 - 2(-3cos(2\u03c0x + 1) + 2) + 4) - 1)/(2(-4(-3cos(2\u03c0x + 1) + 2)^2 - 2(-3cos(2\u03c0x + 1) + 2) + 4) + 2)) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -5((-2(1(2(3x + 4)^2 + 2(3x + 4)) - 3) + 1)/(2(1(2(3x + 4)^2 + 2(3x + 4)) - 3) + 3))^2 - 2((-2(1(2(3x + 4)^2 + 2(3x + 4)) - 3) + 1)/(2(1(2(3x + 4)^2 + 2(3x + 4)) - 3) + 3)) + 3 and g(x) = (2((2(-3(-2x + 1) + 2) - 2)/(-2(-3(-2x + 1) + 2) - 3)) - 2)/(-2((2(-3(-2x + 1) + 2) - 2)/(-2(-3(-2x + 1) + 2) - 3)) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (3(3(-5((1(-3x + 5))/(3(-3x + 5) - 2)) + 1) - 5) - 3)/(2(3(-5((1(-3x + 5))/(3(-3x + 5) - 2)) + 1) - 5) + 3) and g(x) = -2sin(2\u03c0((-1(5(2x^2 - 5x)^2 - 5(2x^2 - 5x) - 5) + 1)/(-2(5(2x^2 - 5x)^2 - 5(2x^2 - 5x) - 5) - 2)) + 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2(-5(1((1(-4x^2 + 2x - 3) - 1)/(3(-4x^2 + 2x - 3)))^2 - 2((1(-4x^2 + 2x - 3) - 1)/(3(-4x^2 + 2x - 3))) + 3) + 3)^2 + 4(-5(1((1(-4x^2 + 2x - 3) - 1)/(3(-4x^2 + 2x - 3)))^2 - 2((1(-4x^2 + 2x - 3) - 1)/(3(-4x^2 + 2x - 3))) + 3) + 3) - 5 and g(x) = -2|(-1(4((-2x - 1)/(1x + 2)) + 3) + 4) - 2| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-2(4(2|((3(-2|x - 1| - 3))/(-2(-2|x - 1| - 3) - 1)) + 3| - 1)^2 + 1(2|((3(-2|x - 1| - 3))/(-2(-2|x - 1| - 3) - 1)) + 3| - 1) - 5) + 3)/(2(4(2|((3(-2|x - 1| - 3))/(-2(-2|x - 1| - 3) - 1)) + 3| - 1)^2 + 1(2|((3(-2|x - 1| - 3))/(-2(-2|x - 1| - 3) - 1)) + 3| - 1) - 5)) and g(x) = (-1(4((2(3|x + 2| + 1) - 1)/(-1(3|x + 2| + 1) - 2)) + 2) + 1)/(2(4((2(3|x + 2| + 1) - 1)/(-1(3|x + 2| + 1) - 2)) + 2) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-1(-1|(-3sin(1\u03c0(-2((-2x - 2)/(-3x - 2))) - 2) + 3) - 2| + 3) - 1)/(3(-1|(-3sin(1\u03c0(-2((-2x - 2)/(-3x - 2))) - 2) + 3) - 2| + 3) - 2) and g(x) = 3(3(3|(-1e^(-2x) - 2)| + 1) + 3) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1|(-5(-4(-5((-1x)/(-3x - 2))^2 + 4((-1x)/(-3x - 2)) + 1)^2 + 2(-5((-1x)/(-3x - 2))^2 + 4((-1x)/(-3x - 2)) + 1) - 2) - 5) - 1| - 2 and g(x) = -5(-2(-4(-5x^2 - 2x - 3)^2 - 4(-5x^2 - 2x - 3))^2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3(3|((3(4((1x - 2)/(-1x + 3))^2 + 4((1x - 2)/(-1x + 3)) - 5) + 3)/(-3(4((1x - 2)/(-1x + 3))^2 + 4((1x - 2)/(-1x + 3)) - 5) + 1)) + 2|) - 4 and g(x) = -1|((-2(1(2x^2 + 5x + 5)^2 - 4(2x^2 + 5x + 5) - 1))/(1(1(2x^2 + 5x + 5)^2 - 4(2x^2 + 5x + 5) - 1) + 1)) + 1| - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-2(-2e^(1((3(1(-2|x - 1| - 2)) - 2)/(3(1(-2|x - 1| - 2)) + 3))) - 3) + 1)/(1(-2e^(1((3(1(-2|x - 1| - 2)) - 2)/(3(1(-2|x - 1| - 2)) + 3))) - 3) + 1) and g(x) = (2((2(4((-2x - 3)/(-2x + 3)) + 3) + 2)/(-2(4((-2x - 3)/(-2x + 3)) + 3) - 3)) + 3)/(-2((2(4((-2x - 3)/(-2x + 3)) + 3) + 2)/(-2(4((-2x - 3)/(-2x + 3)) + 3) - 3)) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3sin(2\u03c0(5(3((1(-1|x| - 2) - 2)/(1(-1|x| - 2))) - 3) - 1) + 3) + 1 and g(x) = 1|(5((1((-1x + 1)/(1x + 2)) - 1)/(1((-1x + 1)/(1x + 2)) - 2)) + 5) + 3| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1((-2(5((2(-3x - 5) + 2)/(-1(-3x - 5) + 3)) + 5) - 1)/(-2(5((2(-3x - 5) + 2)/(-1(-3x - 5) + 3)) + 5) + 3)) + 1 and g(x) = -2e^(-1((1(-5(2x^2 - 2) - 3) - 1)/(1(-5(2x^2 - 2) - 3)))) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3|(3((-1(1(-2sin(3\u03c0x - 1) - 3)^2 - 2(-2sin(3\u03c0x - 1) - 3) + 1) + 1)/(3(1(-2sin(3\u03c0x - 1) - 3)^2 - 2(-2sin(3\u03c0x - 1) - 3) + 1) - 2)) + 2) + 1| + 3 and g(x) = 2|((-1((1((3x + 2)/(-1x + 3)) + 1)/(-2((3x + 2)/(-1x + 3)) - 3)) + 3)/(2((1((3x + 2)/(-1x + 3)) + 1)/(-2((3x + 2)/(-1x + 3)) - 3)) + 1)) + 2| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (1(-1cos(1\u03c0(3(-4(-2x - 1)^2 - 5(-2x - 1) - 2)^2 + 4(-4(-2x - 1)^2 - 5(-2x - 1) - 2) + 2) + 2) + 3))/(-2(-1cos(1\u03c0(3(-4(-2x - 1)^2 - 5(-2x - 1) - 2)^2 + 4(-4(-2x - 1)^2 - 5(-2x - 1) - 2) + 2) + 2) + 3) - 3) and g(x) = (2(-3|(5((-1x - 2)/(2x + 3))^2 - 3((-1x - 2)/(2x + 3)) - 1) + 1| + 1) + 2)/(-2(-3|(5((-1x - 2)/(2x + 3))^2 - 3((-1x - 2)/(2x + 3)) - 1) + 1| + 1) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(-3|(2(-5(2sin(2\u03c0x + 2) + 2) + 5)^2 + 3(-5(2sin(2\u03c0x + 2) + 2) + 5) + 3) + 2|) - 2)/(1(-3|(2(-5(2sin(2\u03c0x + 2) + 2) + 5)^2 + 3(-5(2sin(2\u03c0x + 2) + 2) + 5) + 3) + 2|) + 2) and g(x) = 1((2(-2(1x + 4) - 2) - 2)/(-1(-2(1x + 4) - 2) + 2)) - 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3|(-2cos(1\u03c0(-1(-1|(3x^2 - 1x + 3) - 1| - 3) + 1) + 2) - 3) - 1| + 2 and g(x) = 5(-1(-3((3x + 2)/(2x - 1)) - 5)^2 + 4(-3((3x + 2)/(2x - 1)) - 5) + 2) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -5((-3(5(-3(1x^2 + 1x - 3) + 4)^2 - 3))/(1(5(-3(1x^2 + 1x - 3) + 4)^2 - 3))) and g(x) = (-3(-5((-1((3x)/(-3x + 4)) - 1)/(1((3x)/(-3x + 4)))) + 2) - 1)/(-1(-5((-1((3x)/(-3x + 4)) - 1)/(1((3x)/(-3x + 4)))) + 2) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -5(-1(3|(-1e^(-2((3x + 2)/(1x + 3))) - 1) + 1| + 2) + 1) + 2 and g(x) = (-2(1(-3|((-2x + 1)/(-2x - 3)) + 3| + 2) - 1) - 2)/(2(1(-3|((-2x + 1)/(-2x - 3)) + 3| + 2) - 1) - 1) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 1|((-2(-2|(5((-1x - 1)/(1x)) + 4) + 3| + 1) + 1)/(2(-2|(5((-1x - 1)/(1x)) + 4) + 3| + 1) + 3)) - 2| and g(x) = 4(-5(4(-5x + 4)^2) - 1)^2 + 5(-5(4(-5x + 4)^2) - 1) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (1(1(-1|((-1(-2|x - 3| + 2) + 1)/(2(-2|x - 3| + 2) + 1)) - 1| + 3)^2 - 2(-1|((-1(-2|x - 3| + 2) + 1)/(2(-2|x - 3| + 2) + 1)) - 1| + 3) + 5) - 2)/(-3(1(-1|((-1(-2|x - 3| + 2) + 1)/(2(-2|x - 3| + 2) + 1)) - 1| + 3)^2 - 2(-1|((-1(-2|x - 3| + 2) + 1)/(2(-2|x - 3| + 2) + 1)) - 1| + 3) + 5) + 4) and g(x) = (-1((1(3(3|x + 3| - 3) - 5) - 2)/(-2(3(3|x + 3| - 3) - 5))) - 3)/(-3((1(3(3|x + 3| - 3) - 5) - 2)/(-2(3(3|x + 3| - 3) - 5)))) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|(-4(1(1|(2x + 5)| - 1)^2 + 2(1|(2x + 5)| - 1))^2 - 3(1(1|(2x + 5)| - 1)^2 + 2(1|(2x + 5)| - 1)) - 1) + 1| - 3 and g(x) = 1|(-1|((-1(-1sin(3\u03c0x + 3) + 3) - 1)/(2(-1sin(3\u03c0x + 3) + 3) - 3)) + 3|) + 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -5((2((-2(3(-4x^2 + 2x + 4)^2 + 4(-4x^2 + 2x + 4) - 5) - 2)/(-2(3(-4x^2 + 2x + 4)^2 + 4(-4x^2 + 2x + 4) - 5))) + 3)/(1((-2(3(-4x^2 + 2x + 4)^2 + 4(-4x^2 + 2x + 4) - 5) - 2)/(-2(3(-4x^2 + 2x + 4)^2 + 4(-4x^2 + 2x + 4) - 5))) - 3))^2 + 1((2((-2(3(-4x^2 + 2x + 4)^2 + 4(-4x^2 + 2x + 4) - 5) - 2)/(-2(3(-4x^2 + 2x + 4)^2 + 4(-4x^2 + 2x + 4) - 5))) + 3)/(1((-2(3(-4x^2 + 2x + 4)^2 + 4(-4x^2 + 2x + 4) - 5) - 2)/(-2(3(-4x^2 + 2x + 4)^2 + 4(-4x^2 + 2x + 4) - 5))) - 3)) and g(x) = 1((-3(4(2x + 2)^2 - 1) + 2)/(3(4(2x + 2)^2 - 1))) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 4((-3(-3|(2(2x - 2) + 3) + 1| + 1) - 1)/(-2(-3|(2(2x - 2) + 3) + 1| + 1) + 1)) - 1 and g(x) = (-3((1(1|(3|x - 1| - 2) + 1| + 1))/(-1(1|(3|x - 1| - 2) + 1| + 1) + 2)) + 3)/(-2((1(1|(3|x - 1| - 2) + 1| + 1))/(-1(1|(3|x - 1| - 2) + 1| + 1) + 2)) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -5(1(-2|(3|(-2x^2 - 4x - 3) - 3| + 2) + 3| - 1) + 5)^2 + 5(1(-2|(3|(-2x^2 - 4x - 3) - 3| + 2) + 3| - 1) + 5) and g(x) = -1((2((1(5x - 4))/(1(5x - 4) + 1)) + 2)/(-2((1(5x - 4))/(1(5x - 4) + 1)) + 1))^2 - 1((2((1(5x - 4))/(1(5x - 4) + 1)) + 2)/(-2((1(5x - 4))/(1(5x - 4) + 1)) + 1)) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2(1|(2(-3(4x + 5) + 5)^2 - 2(-3(4x + 5) + 5) - 4)| + 1)^2 - 5(1|(2(-3(4x + 5) + 5)^2 - 2(-3(4x + 5) + 5) - 4)| + 1) - 3 and g(x) = -1(-3|(-2|(2cos(1\u03c0x + 3) - 2) + 2| - 1)| + 3)^2 + 3(-3|(-2|(2cos(1\u03c0x + 3) - 2) + 2| - 1)| + 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -5(-2sin(3\u03c0(-1|(2|(2|x - 3| + 1) - 1| + 3) + 2| - 3) - 3) - 1) + 4 and g(x) = -3|(-1(-2((2x)/(-3x + 1))^2 - 5((2x)/(-3x + 1)) + 3) - 5) - 2| + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (3((-3((2(-3|((1x - 3)/(-1x - 3)) + 1| - 2) + 1)/(-1(-3|((1x - 3)/(-1x - 3)) + 1| - 2) + 2)) + 3)/(-3((2(-3|((1x - 3)/(-1x - 3)) + 1| - 2) + 1)/(-1(-3|((1x - 3)/(-1x - 3)) + 1| - 2) + 2)))) + 1)/(-3((-3((2(-3|((1x - 3)/(-1x - 3)) + 1| - 2) + 1)/(-1(-3|((1x - 3)/(-1x - 3)) + 1| - 2) + 2)) + 3)/(-3((2(-3|((1x - 3)/(-1x - 3)) + 1| - 2) + 1)/(-1(-3|((1x - 3)/(-1x - 3)) + 1| - 2) + 2)))) + 1) and g(x) = -5((-2(1(5x + 3) - 1) - 1)/(3(1(5x + 3) - 1)))^2 + 1((-2(1(5x + 3) - 1) - 1)/(3(1(5x + 3) - 1))) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5(-3|(1(-2(-1|x + 1| - 2) - 5) - 5) + 2| - 2) - 3 and g(x) = (-1(2|(-3(-5x^2 + 5x)^2 - 3(-5x^2 + 5x) - 1) + 3| - 3) + 3)/(-2(2|(-3(-5x^2 + 5x)^2 - 3(-5x^2 + 5x) - 1) + 3| - 3) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -2e^(-1((-2(3(3|(-4x - 4) + 2| - 1) - 1) - 2)/(1(3(3|(-4x - 4) + 2| - 1) - 1) - 3))) + 2 and g(x) = 1|(-1|(2|(-3cos(1\u03c0x - 2) - 2) - 1| - 1) - 3| + 3) + 1| - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(-1(1((1(-2x^2 - 2) - 3)/(-3(-2x^2 - 2) - 3))^2 - 4((1(-2x^2 - 2) - 3)/(-3(-2x^2 - 2) - 3)) - 3) - 4) - 2 and g(x) = -2(1(-2((-2x - 2)/(-1x - 1))^2 + 2((-2x - 2)/(-1x - 1)) + 5)^2 + 2(-2((-2x - 2)/(-1x - 1))^2 + 2((-2x - 2)/(-1x - 1)) + 5) + 5) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -4((-3(1|(-4(-1cos(2\u03c0x - 2) + 1) - 2) - 3| - 3) + 2)/(1(1|(-4(-1cos(2\u03c0x - 2) + 1) - 2) - 3| - 3) + 1)) + 5 and g(x) = -4(1(2|(-3x - 2) + 2| - 3) - 5) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 1(-3|(-5(3|((-1x - 2)/(1x + 1)) - 1|) + 1) - 2| - 3) and g(x) = -2(2(1((1x - 1)/(-2x - 3))^2 - 3)^2 + 1(1((1x - 1)/(-2x - 3))^2 - 3) - 4) + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-2(5(3((-1((1x + 1)/(2x)) + 1)/(2((1x + 1)/(2x)) + 2)) - 2)^2 - 2(3((-1((1x + 1)/(2x)) + 1)/(2((1x + 1)/(2x)) + 2)) - 2) - 3))/(3(5(3((-1((1x + 1)/(2x)) + 1)/(2((1x + 1)/(2x)) + 2)) - 2)^2 - 2(3((-1((1x + 1)/(2x)) + 1)/(2((1x + 1)/(2x)) + 2)) - 2) - 3) - 2) and g(x) = -3(1((2((-1x - 2)/(-1x - 1)) + 1)/(-3((-1x - 2)/(-1x - 1)) + 1))^2 + 2)^2 + 3(1((2((-1x - 2)/(-1x - 1)) + 1)/(-3((-1x - 2)/(-1x - 1)) + 1))^2 + 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1cos(1\u03c0(1(-4(5(-3|x - 1|) - 5)^2 - 1(5(-3|x - 1|) - 5) + 5) - 5) + 1) - 3 and g(x) = (-2(2|(-5((-2x)/(2x - 1)) + 5) - 2| - 2) - 1)/(-1(2|(-5((-2x)/(2x - 1)) + 5) - 2| - 2)) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(-4((-2(2|(-3|x - 2| - 2) + 3| + 3) + 1)/(-2(2|(-3|x - 2| - 2) + 3| + 3) - 3))^2 - 4((-2(2|(-3|x - 2| - 2) + 3| + 3) + 1)/(-2(2|(-3|x - 2| - 2) + 3| + 3) - 3)) - 3)^2 - 4(-4((-2(2|(-3|x - 2| - 2) + 3| + 3) + 1)/(-2(2|(-3|x - 2| - 2) + 3| + 3) - 3))^2 - 4((-2(2|(-3|x - 2| - 2) + 3| + 3) + 1)/(-2(2|(-3|x - 2| - 2) + 3| + 3) - 3)) - 3) + 5 and g(x) = -3(4((-3(-2|x - 1| + 3))/(2(-2|x - 1| + 3) + 2))) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|((3(-3cos(1\u03c0(2((-1x - 3)/(-3x + 4))^2 + 5((-1x - 3)/(-3x + 4)) - 2) + 3) - 1) - 2)/(2(-3cos(1\u03c0(2((-1x - 3)/(-3x + 4))^2 + 5((-1x - 3)/(-3x + 4)) - 2) + 3) - 1) - 1)) - 2| + 3 and g(x) = 3|(-2|((-3(5x - 1) + 2)/(3(5x - 1) - 1)) - 3| + 2) + 1| - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 1(1|(-1e^(-2(-1|(-3x^2 + 4x) - 2| + 3)) - 2) + 3| - 3) - 3 and g(x) = -5(-1(5((-3x + 2)/(-2x + 3)) - 5))^2 + 5(-1(5((-3x + 2)/(-2x + 3)) - 5)) - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -3(-3|(5(3(-4x^2 + 4x - 2) + 4)^2 + 4(3(-4x^2 + 4x - 2) + 4) + 4)| + 1)^2 - 5(-3|(5(3(-4x^2 + 4x - 2) + 4)^2 + 4(3(-4x^2 + 4x - 2) + 4) + 4)| + 1) - 4 and g(x) = -2e^(-1((2(-2(1x^2 + 2x) + 5) - 2)/(-3(-2(1x^2 + 2x) + 5)))) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1(2((-3(3(1x + 1) - 4) - 2)/(-2(3(1x + 1) - 4) + 1)) - 2) + 2 and g(x) = 5(-1cos(1\u03c0(-3|(5x^2 - 2x - 1) - 2| - 2) + 2) - 2) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3((2(-3|((-2((3x + 2)/(1x + 3)))/(-1((3x + 2)/(1x + 3)) - 1)) + 2| + 3) + 2)/(-1(-3|((-2((3x + 2)/(1x + 3)))/(-1((3x + 2)/(1x + 3)) - 1)) + 2| + 3) - 2)) + 1)/(-2((2(-3|((-2((3x + 2)/(1x + 3)))/(-1((3x + 2)/(1x + 3)) - 1)) + 2| + 3) + 2)/(-1(-3|((-2((3x + 2)/(1x + 3)))/(-1((3x + 2)/(1x + 3)) - 1)) + 2| + 3) - 2))) and g(x) = 2(1cos(2\u03c0(-1(-3|x - 3| - 2)^2 + 5(-3|x - 3| - 2) - 2) + 3) + 2) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (-3(3|((-2(3e^(-1(-1x - 2))) + 2)/(2(3e^(-1(-1x - 2))) + 2)) + 3| + 3) - 1)/(-2(3|((-2(3e^(-1(-1x - 2))) + 2)/(2(3e^(-1(-1x - 2))) + 2)) + 3| + 3) + 3) and g(x) = 3sin(3\u03c0((-2(2|((3x - 1)/(1x + 3)) + 1| + 3) - 3)/(1(2|((3x - 1)/(1x + 3)) + 1| + 3) + 2)) + 1) + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 5(2sin(2\u03c0(-1|((3(3x^2 - 2x + 2) - 1)/(2(3x^2 - 2x + 2) - 3)) - 2| - 1) - 3) + 1) + 5 and g(x) = (2(2|(4(-1x + 2) + 1) - 1| - 2) + 1)/(-3(2|(4(-1x + 2) + 1) - 1| - 2) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-3(-1(-1(3e^(1((1x + 2)/(2x + 2))))^2 + 2(3e^(1((1x + 2)/(2x + 2)))) + 2)^2 - 4(-1(3e^(1((1x + 2)/(2x + 2))))^2 + 2(3e^(1((1x + 2)/(2x + 2)))) + 2) - 2) - 2)/(-1(-1(-1(3e^(1((1x + 2)/(2x + 2))))^2 + 2(3e^(1((1x + 2)/(2x + 2)))) + 2)^2 - 4(-1(3e^(1((1x + 2)/(2x + 2))))^2 + 2(3e^(1((1x + 2)/(2x + 2)))) + 2) - 2) - 3) and g(x) = (3((-1((-1(-2sin(2\u03c0x) + 3) + 1)/(3(-2sin(2\u03c0x) + 3) - 2)) - 2)/(1((-1(-2sin(2\u03c0x) + 3) + 1)/(3(-2sin(2\u03c0x) + 3) - 2)) + 1)) + 1)/(-1((-1((-1(-2sin(2\u03c0x) + 3) + 1)/(3(-2sin(2\u03c0x) + 3) - 2)) - 2)/(1((-1(-2sin(2\u03c0x) + 3) + 1)/(3(-2sin(2\u03c0x) + 3) - 2)) + 1)) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(1((-3(2|(4x^2 + 3x - 1) - 2| + 3) - 2)/(1(2|(4x^2 + 3x - 1) - 2| + 3))) + 3) + 3)/(-3(1((-3(2|(4x^2 + 3x - 1) - 2| + 3) - 2)/(1(2|(4x^2 + 3x - 1) - 2| + 3))) + 3)) and g(x) = 3((1((-3((-2x + 1)/(-2x + 3)) + 1)/(-2((-2x + 1)/(-2x + 3)) - 1)) + 3)/(1((-3((-2x + 1)/(-2x + 3)) + 1)/(-2((-2x + 1)/(-2x + 3)) - 1)) - 3)) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (1((-2(-4((3(2x) - 1)/(1(2x) - 2))^2 - 3((3(2x) - 1)/(1(2x) - 2)) + 1))/(-1(-4((3(2x) - 1)/(1(2x) - 2))^2 - 3((3(2x) - 1)/(1(2x) - 2)) + 1) - 2)) - 1)/(2((-2(-4((3(2x) - 1)/(1(2x) - 2))^2 - 3((3(2x) - 1)/(1(2x) - 2)) + 1))/(-1(-4((3(2x) - 1)/(1(2x) - 2))^2 - 3((3(2x) - 1)/(1(2x) - 2)) + 1) - 2)) + 2) and g(x) = -3|((3(4(-3|x| + 1) - 5))/(3(4(-3|x| + 1) - 5) - 1)) - 2| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(-1|(-3|(-5(1x^2 + 4) + 2) + 1| - 1) - 2| + 1) + 5 and g(x) = 4(3e^(1(2(1|x| + 2)^2 - 4(1|x| + 2))) + 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 5((-3(2((-1(1cos(1\u03c0x - 2) - 1) + 2)/(2(1cos(1\u03c0x - 2) - 1) + 2)) - 1))/(1(2((-1(1cos(1\u03c0x - 2) - 1) + 2)/(2(1cos(1\u03c0x - 2) - 1) + 2)) - 1))) and g(x) = -5(1(3((-2x - 2)/(3x - 2))) + 3) + 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-2((3(-1|(-2(-3e^(2x) + 2) + 2) + 1| + 2))/(-3(-1|(-2(-3e^(2x) + 2) + 2) + 1| + 2) - 3)) - 2)/(1((3(-1|(-2(-3e^(2x) + 2) + 2) + 1| + 2))/(-3(-1|(-2(-3e^(2x) + 2) + 2) + 1| + 2) - 3)) + 3) and g(x) = -5(-5((1(2x) + 2)/(-3(2x) + 2))^2 - 4((1(2x) + 2)/(-3(2x) + 2)) + 2) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 4(-2(-4(-3cos(2\u03c0((1x - 1)/(-1x + 2)) + 2) - 2)^2 + 4)^2 + 5(-4(-3cos(2\u03c0((1x - 1)/(-1x + 2)) + 2) - 2)^2 + 4) + 3)^2 + 1(-2(-4(-3cos(2\u03c0((1x - 1)/(-1x + 2)) + 2) - 2)^2 + 4)^2 + 5(-4(-3cos(2\u03c0((1x - 1)/(-1x + 2)) + 2) - 2)^2 + 4) + 3) + 2 and g(x) = 1(3(5((3x)/(-1x - 1))) + 4) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2sin(2\u03c0(3|(-3(1|((3x - 1)/(3x + 2)) - 1| + 3) + 1) + 3| + 1) - 2) + 2 and g(x) = (2((1(-4(3|x - 1| - 1) - 3) + 3)/(3(-4(3|x - 1| - 1) - 3) + 1)) + 1)/(-3((1(-4(3|x - 1| - 1) - 3) + 3)/(3(-4(3|x - 1| - 1) - 3) + 1)) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3sin(2\u03c0((1(4((3(-1|x - 3| - 2))/(-3(-1|x - 3| - 2) - 3))^2 + 2((3(-1|x - 3| - 2))/(-3(-1|x - 3| - 2) - 3)) + 5) + 1)/(3(4((3(-1|x - 3| - 2))/(-3(-1|x - 3| - 2) - 3))^2 + 2((3(-1|x - 3| - 2))/(-3(-1|x - 3| - 2) - 3)) + 5) - 2)) + 3) + 1 and g(x) = (3((-2((-1(-1|x - 2| + 2))/(-1(-1|x - 2| + 2) + 2)) - 2)/(-1((-1(-1|x - 2| + 2))/(-1(-1|x - 2| + 2) + 2)) + 2)) - 1)/(-1((-2((-1(-1|x - 2| + 2))/(-1(-1|x - 2| + 2) + 2)) - 2)/(-1((-1(-1|x - 2| + 2))/(-1(-1|x - 2| + 2) + 2)) + 2)) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 4((2((-3(-4(2x - 1)^2 + 4(2x - 1) + 4))/(-3(-4(2x - 1)^2 + 4(2x - 1) + 4) - 1)) + 2)/(3((-3(-4(2x - 1)^2 + 4(2x - 1) + 4))/(-3(-4(2x - 1)^2 + 4(2x - 1) + 4) - 1)) - 2))^2 + 5((2((-3(-4(2x - 1)^2 + 4(2x - 1) + 4))/(-3(-4(2x - 1)^2 + 4(2x - 1) + 4) - 1)) + 2)/(3((-3(-4(2x - 1)^2 + 4(2x - 1) + 4))/(-3(-4(2x - 1)^2 + 4(2x - 1) + 4) - 1)) - 2)) - 5 and g(x) = -4(-3((2(4x + 2) - 3)/(-2(4x + 2) - 1))^2 + 5) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3cos(3\u03c0((1(2((-1((-2x - 3)/(1x)) + 1)/(2((-2x - 3)/(1x)) + 1)) + 4) - 3)/(-2(2((-1((-2x - 3)/(1x)) + 1)/(2((-2x - 3)/(1x)) + 1)) + 4) - 1))) - 3 and g(x) = (-3((2(-5(-5x - 2)) - 3)/(1(-5(-5x - 2)))) - 2)/(-1((2(-5(-5x - 2)) - 3)/(1(-5(-5x - 2)))) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1(-1(3e^(1((1(-2|x + 2| - 1) + 3)/(2(-2|x + 2| - 1) - 1))) - 1) - 5) + 3 and g(x) = (3(1(1|(2x^2 - 2x - 4) + 3| - 1)^2 - 5(1|(2x^2 - 2x - 4) + 3| - 1)) - 1)/(-2(1(1|(2x^2 - 2x - 4) + 3| - 1)^2 - 5(1|(2x^2 - 2x - 4) + 3| - 1))) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-1(3(1|((-1(-1cos(3\u03c0x) + 3) - 2)/(-3(-1cos(3\u03c0x) + 3) - 3)) - 2| + 3) - 5) - 2)/(-1(3(1|((-1(-1cos(3\u03c0x) + 3) - 2)/(-3(-1cos(3\u03c0x) + 3) - 3)) - 2| + 3) - 5) - 1) and g(x) = (1(-5((-1((-1x - 2)/(2x + 3)) - 2)/(-1((-1x - 2)/(2x + 3)) - 1)) + 2) + 3)/(2(-5((-1((-1x - 2)/(2x + 3)) - 2)/(-1((-1x - 2)/(2x + 3)) - 1)) + 2) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2(1e^(1(-5(-4(-3x^2 - 4x - 2) + 2) - 4))) + 4 and g(x) = (3(2|(-2|(-2e^(2x)) - 3| + 3) + 3| - 1) - 2)/(3(2|(-2|(-2e^(2x)) - 3| + 3) + 3| - 1) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2(3|(-1(-2e^(-2(-1x^2 + 3x + 3)) - 2)^2 + 5(-2e^(-2(-1x^2 + 3x + 3)) - 2) + 4)| + 2) - 2 and g(x) = 1|(5(5(-1x^2 - 1x - 2)^2 - 1(-1x^2 - 1x - 2) - 2)^2 - 1)| + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1|(4(-4(-3(5x^2 - 5x - 1)^2 + 5(5x^2 - 5x - 1) - 2) + 1) + 2) + 2| + 2 and g(x) = 4(2|(-2(3e^(-1x) + 1)^2 - 1(3e^(-1x) + 1) - 2) - 1|)^2 - 5(2|(-2(3e^(-1x) + 1)^2 - 1(3e^(-1x) + 1) - 2) - 1|) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -2(-2(1(1|(-2e^(2x)) - 2| - 2) - 2)^2 + 3(1(1|(-2e^(2x)) - 2| - 2) - 2) - 4)^2 - 2(-2(1(1|(-2e^(2x)) - 2| - 2) - 2)^2 + 3(1(1|(-2e^(2x)) - 2| - 2) - 2) - 4) - 5 and g(x) = -3((-2(5(-2|x - 2| + 3)^2 - 2(-2|x - 2| + 3) - 5) - 2)/(1(5(-2|x - 2| + 3)^2 - 2(-2|x - 2| + 3) - 5) - 3)) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-3(3(2(-3(3e^(2x) + 1) + 1) - 3) - 5))/(-2(3(2(-3(3e^(2x) + 1) + 1) - 3) - 5) + 3) and g(x) = 1|((2(2((2x + 2)/(3x - 1)) - 3) - 2)/(-1(2((2x + 2)/(3x - 1)) - 3) - 1)) + 3| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 1|((2(1|(2|(3x^2 - 5x + 5)| - 2) + 2| - 3) - 3)/(-2(1|(2|(3x^2 - 5x + 5)| - 2) + 2| - 3) - 1)) - 3| - 1 and g(x) = (2((2(2(2x + 2)^2 - 2(2x + 2) - 5) - 2)/(-3(2(2x + 2)^2 - 2(2x + 2) - 5))) - 3)/(1((2(2(2x + 2)^2 - 2(2x + 2) - 5) - 2)/(-3(2(2x + 2)^2 - 2(2x + 2) - 5))) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 4((-1(-1(4(-5x - 5) - 4) - 2) - 2)/(1(-1(4(-5x - 5) - 4) - 2)))^2 - 2((-1(-1(4(-5x - 5) - 4) - 2) - 2)/(1(-1(4(-5x - 5) - 4) - 2))) - 5 and g(x) = 1|(1(1|(4x^2 + 4x + 5) + 1|) - 3) - 1| meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1|(-5(-2e^(-1(1(-1|x + 2|)^2 - 5(-1|x + 2|) - 5)) - 2)^2 - 3(-2e^(-1(1(-1|x + 2|)^2 - 5(-1|x + 2|) - 5)) - 2) - 2) + 3| - 1 and g(x) = -1(1|(2|(-2|x + 1| - 3) + 1| + 1) - 2| - 3)^2 - 4(1|(2|(-2|x + 1| - 3) + 1| + 1) - 2| - 3) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3(3|(-4(3((3x + 3)/(-3x + 4)) + 4)^2 - 4(3((3x + 3)/(-3x + 4)) + 4) + 4) - 3| + 1) and g(x) = -4((-1(-2|((-1x - 1)/(-3x - 3)) + 1| - 3) - 3)/(-2(-2|((-1x - 1)/(-3x - 3)) + 1| - 3) + 3))^2 + 3((-1(-2|((-1x - 1)/(-3x - 3)) + 1| - 3) - 3)/(-2(-2|((-1x - 1)/(-3x - 3)) + 1| - 3) + 3)) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2(-1((3(2|(-3x) + 3|) + 1)/(2(2|(-3x) + 3|) - 3)) - 1) - 5 and g(x) = 3(3|((2(3|x + 3| + 3) - 3)/(-1(3|x + 3| + 3) + 2)) - 1|) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3((1(3|((2(-1x^2 + 3x + 2) + 2)/(-2(-1x^2 + 3x + 2) - 2)) - 2| + 3) + 3)/(-1(3|((2(-1x^2 + 3x + 2) + 2)/(-2(-1x^2 + 3x + 2) - 2)) - 2| + 3) + 3)) + 1 and g(x) = (-3(-2|(1((3x)/(2x + 3)) + 3) + 1| + 2) - 2)/(-1(-2|(1((3x)/(2x + 3)) + 3) + 1| + 2) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-2(2(-1|(5((-2x - 1)/(-1x + 2)) - 4) - 3| - 1) + 4) - 3)/(2(2(-1|(5((-2x - 1)/(-1x + 2)) - 4) - 3| - 1) + 4) - 3) and g(x) = 1(-1(1|(1x^2 + 4x + 3) + 2| - 1)^2 + 1(1|(1x^2 + 4x + 3) + 2| - 1) - 1) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2(5(3(5(-3|x + 3| - 1) - 1)^2 - 4(5(-3|x + 3| - 1) - 1) + 2)^2 + 2(3(5(-3|x + 3| - 1) - 1)^2 - 4(5(-3|x + 3| - 1) - 1) + 2) + 5) + 5 and g(x) = -3(3(-3(-3|x - 1| - 2)^2 - 4(-3|x - 1| - 2) + 3) - 3)^2 - 5(3(-3(-3|x - 1| - 2)^2 - 4(-3|x - 1| - 2) + 3) - 3) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1(1(4((-3((-1x + 3)/(-2x - 2)))/(-1((-1x + 3)/(-2x - 2)) - 3))^2 + 3((-3((-1x + 3)/(-2x - 2)))/(-1((-1x + 3)/(-2x - 2)) - 3)) - 5)^2 + 2(4((-3((-1x + 3)/(-2x - 2)))/(-1((-1x + 3)/(-2x - 2)) - 3))^2 + 3((-3((-1x + 3)/(-2x - 2)))/(-1((-1x + 3)/(-2x - 2)) - 3)) - 5) - 4) and g(x) = (-3(-1(1e^(-2(2x^2 + 3x + 2)) - 2) - 3) + 2)/(2(-1(1e^(-2(2x^2 + 3x + 2)) - 2) - 3) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-3(3(-2(-5(1x + 1)^2 - 2(1x + 1) - 3)) - 1) + 1)/(3(3(-2(-5(1x + 1)^2 - 2(1x + 1) - 3)) - 1) - 2) and g(x) = -1(1((1(-1e^(1x) + 3) - 2)/(1(-1e^(1x) + 3) + 3))^2 + 4((1(-1e^(1x) + 3) - 2)/(1(-1e^(1x) + 3) + 3))) + 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2|((-2((-2(-1cos(2\u03c0(-4x - 4)) - 3) + 2)/(1(-1cos(2\u03c0(-4x - 4)) - 3))) - 1)/(2((-2(-1cos(2\u03c0(-4x - 4)) - 3) + 2)/(1(-1cos(2\u03c0(-4x - 4)) - 3))) + 3)) + 3| - 2 and g(x) = -3((-1((-3((-2x - 2)/(-3x + 4)) + 1)/(-3((-2x - 2)/(-3x + 4)) - 1)) - 3)/(2((-3((-2x - 2)/(-3x + 4)) + 1)/(-3((-2x - 2)/(-3x + 4)) - 1)) + 1))^2 + 4((-1((-3((-2x - 2)/(-3x + 4)) + 1)/(-3((-2x - 2)/(-3x + 4)) - 1)) - 3)/(2((-3((-2x - 2)/(-3x + 4)) + 1)/(-3((-2x - 2)/(-3x + 4)) - 1)) + 1)) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2cos(3\u03c0((-2(-2|(-3(-2x^2 - 5)^2 + 5(-2x^2 - 5) + 3) + 3| + 2) + 2)/(-1(-2|(-3(-2x^2 - 5)^2 + 5(-2x^2 - 5) + 3) + 3| + 2) + 2)) - 1) - 2 and g(x) = 1(4((-2(1x + 4) + 3)/(1(1x + 4) - 3))^2 - 4((-2(1x + 4) + 3)/(1(1x + 4) - 3)) + 1)^2 - 2(4((-2(1x + 4) + 3)/(1(1x + 4) - 3))^2 - 4((-2(1x + 4) + 3)/(1(1x + 4) - 3)) + 1) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 4(5(-2|(-1(-1x - 5)^2 + 2(-1x - 5) + 1) + 1| + 2) - 2)^2 - 5 and g(x) = 2sin(3\u03c0(-3(3(3|x + 1| - 1)^2 + 5(3|x + 1| - 1) + 1)^2 + 2(3(3|x + 1| - 1)^2 + 5(3|x + 1| - 1) + 1) + 2) + 1) + 1 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 3(-1|(-5(1|(-1x + 3) + 3| - 2) - 1) - 3| + 1)^2 - 5(-1|(-5(1|(-1x + 3) + 3| - 2) - 1) - 3| + 1) + 4 and g(x) = 2|(-2(-3(-4x - 1)^2 - 3(-4x - 1) + 4)) + 1| + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -5((-2(-4(-2(-3|x - 1| + 1)^2 + 5(-3|x - 1| + 1) + 4) + 5))/(2(-4(-2(-3|x - 1| + 1)^2 + 5(-3|x - 1| + 1) + 4) + 5) + 2)) + 1 and g(x) = (2(-2|((3(-3|x + 2| - 2) - 2)/(1(-3|x + 2| - 2) + 2)) - 2| + 2) - 3)/(-1(-2|((3(-3|x + 2| - 2) - 2)/(1(-3|x + 2| - 2) + 2)) - 2| + 2)) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -5((-2(3(-2|(-2x - 3) - 2| + 2)^2 - 5(-2|(-2x - 3) - 2| + 2) - 4))/(1(3(-2|(-2x - 3) - 2| + 2)^2 - 5(-2|(-2x - 3) - 2| + 2) - 4) + 1)) - 1 and g(x) = (3((1(2|(1x^2 - 3x - 1) + 3| + 3))/(3(2|(1x^2 - 3x - 1) + 3| + 3) + 2)) - 3)/(2((1(2|(1x^2 - 3x - 1) + 3| + 3))/(3(2|(1x^2 - 3x - 1) + 3| + 3) + 2))) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -2(-1(3|(-2e^(-2((-1x - 2)/(-3x)))) + 1| - 3) - 2)^2 + 1(-1(3|(-2e^(-2((-1x - 2)/(-3x)))) + 1| - 3) - 2) + 3 and g(x) = (-3((-3((-1(2x^2 - 3x + 5))/(-3(2x^2 - 3x + 5) + 2)) - 1)/(-3((-1(2x^2 - 3x + 5))/(-3(2x^2 - 3x + 5) + 2)) - 3)) + 3)/(1((-3((-1(2x^2 - 3x + 5))/(-3(2x^2 - 3x + 5) + 2)) - 1)/(-3((-1(2x^2 - 3x + 5))/(-3(2x^2 - 3x + 5) + 2)) - 3)) - 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2|((-2(2sin(2\u03c0(-3(-5x^2 - 5)) + 1)) + 2)/(3(2sin(2\u03c0(-3(-5x^2 - 5)) + 1)) + 2)) - 2| + 2 and g(x) = 2sin(3\u03c0(-1(4(4x^2 + 2x)^2 + 4(4x^2 + 2x) + 2)^2 + 5(4(4x^2 + 2x)^2 + 4(4x^2 + 2x) + 2) + 2) + 2) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(5(-1(1(-5x^2 + 3x)^2 - 4(-5x^2 + 3x) + 2) + 4) - 5) + 4 and g(x) = 1(-2(3(1|x - 1| - 3) - 5)^2 + 3) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2|(2((1(1(-5x - 2)^2 + 1(-5x - 2) + 3) - 2)/(3(1(-5x - 2)^2 + 1(-5x - 2) + 3)))^2 + 3((1(1(-5x - 2)^2 + 1(-5x - 2) + 3) - 2)/(3(1(-5x - 2)^2 + 1(-5x - 2) + 3))) + 1)| + 1 and g(x) = (-1((-2(1(3x + 2)^2 - 5(3x + 2) - 2) - 3)/(1(1(3x + 2)^2 - 5(3x + 2) - 2))) + 3)/(-1((-2(1(3x + 2)^2 - 5(3x + 2) - 2) - 3)/(1(1(3x + 2)^2 - 5(3x + 2) - 2)))) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-3(-3|((1(-5(2x + 1)^2 + 5(2x + 1) + 3) - 1)/(-2(-5(2x + 1)^2 + 5(2x + 1) + 3) - 3)) + 2| + 2) - 2)/(3(-3|((1(-5(2x + 1)^2 + 5(2x + 1) + 3) - 1)/(-2(-5(2x + 1)^2 + 5(2x + 1) + 3) - 3)) + 2| + 2) - 2) and g(x) = -1e^(1(1|(1(-3|x - 3| + 3) - 3) + 2| - 2)) + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -1((-3(5(-1|(5x^2 - 2x + 5) - 1| + 2)^2 - 4(-1|(5x^2 - 2x + 5) - 1| + 2) + 2) - 1)/(1(5(-1|(5x^2 - 2x + 5) - 1| + 2)^2 - 4(-1|(5x^2 - 2x + 5) - 1| + 2) + 2)))^2 - 4((-3(5(-1|(5x^2 - 2x + 5) - 1| + 2)^2 - 4(-1|(5x^2 - 2x + 5) - 1| + 2) + 2) - 1)/(1(5(-1|(5x^2 - 2x + 5) - 1| + 2)^2 - 4(-1|(5x^2 - 2x + 5) - 1| + 2) + 2))) + 3 and g(x) = 3|(-3e^(1(-1|(-3x + 5) + 2| + 3)) + 2) - 1| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -5(-5((2(2((-3x - 1)/(3x - 1)) - 1) - 1)/(-1(2((-3x - 1)/(3x - 1)) - 1) - 2)) - 2) + 5 and g(x) = -1((-3(3(-1cos(1\u03c0x + 1) + 2)^2 - 3(-1cos(1\u03c0x + 1) + 2) - 1) - 2)/(3(3(-1cos(1\u03c0x + 1) + 2)^2 - 3(-1cos(1\u03c0x + 1) + 2) - 1) + 2)) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2|(3(-1(-2sin(1\u03c0(3|x - 1|) + 1) + 3)^2 + 5(-2sin(1\u03c0(3|x - 1|) + 1) + 3))) + 1| - 1 and g(x) = 1((-2((-2((1x)/(3x - 2)) - 1)/(1((1x)/(3x - 2)) + 3)) + 3)/(3((-2((1x)/(3x - 2)) - 1)/(1((1x)/(3x - 2)) + 3)) - 2)) + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3|(2|((-1(-3|(2sin(2\u03c0x + 2)) - 3| - 3) + 1)/(1(-3|(2sin(2\u03c0x + 2)) - 3| - 3) - 2)) - 2| - 3) - 1| + 3 and g(x) = (-1(1(4(-4x^2 - 5x + 2)^2 - 4(-4x^2 - 5x + 2) - 4)^2 - 4(4(-4x^2 - 5x + 2)^2 - 4(-4x^2 - 5x + 2) - 4) - 4))/(-1(1(4(-4x^2 - 5x + 2)^2 - 4(-4x^2 - 5x + 2) - 4)^2 - 4(4(-4x^2 - 5x + 2)^2 - 4(-4x^2 - 5x + 2) - 4) - 4) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -3((2(4((3(3x - 3) - 2)/(2(3x - 3) + 1))^2 - 5((3(3x - 3) - 2)/(2(3x - 3) + 1)) + 4))/(2(4((3(3x - 3) - 2)/(2(3x - 3) + 1))^2 - 5((3(3x - 3) - 2)/(2(3x - 3) + 1)) + 4) - 3))^2 + 3((2(4((3(3x - 3) - 2)/(2(3x - 3) + 1))^2 - 5((3(3x - 3) - 2)/(2(3x - 3) + 1)) + 4))/(2(4((3(3x - 3) - 2)/(2(3x - 3) + 1))^2 - 5((3(3x - 3) - 2)/(2(3x - 3) + 1)) + 4) - 3)) + 1 and g(x) = -5(-1|(-2|((3x + 1)/(2x - 1))| - 1) + 3| + 3) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 2|(2(-3(-1e^(-1(1x + 3)) + 2) - 1) + 1)| - 1 and g(x) = -2((3(1sin(1\u03c0(2x^2 + 5x + 4) - 3) + 2) - 1)/(3(1sin(1\u03c0(2x^2 + 5x + 4) - 3) + 2) + 3))^2 + 1((3(1sin(1\u03c0(2x^2 + 5x + 4) - 3) + 2) - 1)/(3(1sin(1\u03c0(2x^2 + 5x + 4) - 3) + 2) + 3)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3((-3((-2(-1(-2x^2 + 2x - 5)^2 - 2(-2x^2 + 2x - 5) - 2) + 3)/(-2(-1(-2x^2 + 2x - 5)^2 - 2(-2x^2 + 2x - 5) - 2) + 3)) + 2)/(2((-2(-1(-2x^2 + 2x - 5)^2 - 2(-2x^2 + 2x - 5) - 2) + 3)/(-2(-1(-2x^2 + 2x - 5)^2 - 2(-2x^2 + 2x - 5) - 2) + 3)) + 1)) - 2 and g(x) = (-2(-1(1|((-2x - 1)/(2x)) - 2| - 3) + 2))/(-3(-1(1|((-2x - 1)/(2x)) - 2| - 3) + 2) + 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 5(4(-1|(2|((1x + 3)/(-3x - 2)) + 1|)|) - 4) - 4 and g(x) = -1|(5((3((-3x + 3)/(-1x - 3)) - 2)/(2((-3x + 3)/(-1x - 3)) + 1))^2 + 1((3((-3x + 3)/(-1x - 3)) - 2)/(2((-3x + 3)/(-1x - 3)) + 1))) - 1| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5((2((1(1(1|x + 1| - 3) - 5) + 2)/(3(1(1|x + 1| - 3) - 5) + 3)) - 1)/(3((1(1(1|x + 1| - 3) - 5) + 2)/(3(1(1|x + 1| - 3) - 5) + 3)) + 1)) + 1 and g(x) = 4(3((-2(2e^(2x) + 1) + 2)/(1(2e^(2x) + 1) + 2)))^2 + 5(3((-2(2e^(2x) + 1) + 2)/(1(2e^(2x) + 1) + 2))) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2|(-2|((-1((-3(1|x + 1| + 1) - 2)/(3(1|x + 1| + 1) + 2)) + 1)/(3((-3(1|x + 1| + 1) - 2)/(3(1|x + 1| + 1) + 2)))) + 3| + 3) + 2| + 3 and g(x) = 5(3((-2(-1|x - 1| + 1) - 1)/(3(-1|x - 1| + 1))) + 4) + 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(1|(3|((2((3x + 3)/(-1x + 2)) + 3)/(-3((3x + 3)/(-1x + 2)) - 1)) + 3| + 3) - 3|) + 2| - 1 and g(x) = -4(1|(-3e^(-2(-1x^2 - 5x - 3))) + 2| - 2) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|(-5((-1(-2cos(2\u03c0(-2|x - 2| - 1) - 3) - 3) + 1)/(-3(-2cos(2\u03c0(-2|x - 2| - 1) - 3) - 3) - 1))^2 - 2((-1(-2cos(2\u03c0(-2|x - 2| - 1) - 3) - 3) + 1)/(-3(-2cos(2\u03c0(-2|x - 2| - 1) - 3) - 3) - 1)) - 1) + 1| - 2 and g(x) = -2|(2e^(-2(2(-1|x|) + 1)) + 1) - 1| + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (1(5((-3(3(-1|x + 2| + 3) - 3) + 3)/(-2(3(-1|x + 2| + 3) - 3) + 3)) + 5) - 2)/(-3(5((-3(3(-1|x + 2| + 3) - 3) + 3)/(-2(3(-1|x + 2| + 3) - 3) + 3)) + 5) + 1) and g(x) = -1|(-2(-1e^(-1((1x + 3)/(-1x))) + 1)^2 - 2(-1e^(-1((1x + 3)/(-1x))) + 1) - 5) - 2| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1|((3(-1(3|(-1x^2 - 2x + 2) - 3| - 1) + 3) - 3)/(3(-1(3|(-1x^2 - 2x + 2) - 3| - 1) + 3))) + 3| - 1 and g(x) = 1(1e^(-2(-2|(1x + 4) + 2| + 2)) - 2)^2 + 4(1e^(-2(-2|(1x + 4) + 2| + 2)) - 2) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-12", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2sin(3\u03c0((-3(-3(-1((1x - 3)/(-3x - 3))^2 - 3((1x - 3)/(-3x - 3)) - 5)^2 + 1(-1((1x - 3)/(-3x - 3))^2 - 3((1x - 3)/(-3x - 3)) - 5) - 1) - 3)/(1(-3(-1((1x - 3)/(-3x - 3))^2 - 3((1x - 3)/(-3x - 3)) - 5)^2 + 1(-1((1x - 3)/(-3x - 3))^2 - 3((1x - 3)/(-3x - 3)) - 5) - 1) + 2)) + 2) + 2 and g(x) = -2(-5(-5(-2e^(1x) + 1) - 3)^2 + 5(-5(-2e^(1x) + 1) - 3) + 5) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2|((-1(2((2((2x + 1)/(-2x + 3)) + 3)/(-2((2x + 1)/(-2x + 3)) + 3))^2 + 4((2((2x + 1)/(-2x + 3)) + 3)/(-2((2x + 1)/(-2x + 3)) + 3)) + 1))/(1(2((2((2x + 1)/(-2x + 3)) + 3)/(-2((2x + 1)/(-2x + 3)) + 3))^2 + 4((2((2x + 1)/(-2x + 3)) + 3)/(-2((2x + 1)/(-2x + 3)) + 3)) + 1) + 3)) + 1| + 1 and g(x) = (2(3(-3(-1e^(2x) + 1)^2 - 1(-1e^(2x) + 1) + 1) + 2) - 3)/(-1(3(-3(-1e^(2x) + 1)^2 - 1(-1e^(2x) + 1) + 1) + 2) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-3((1((-2(1(5x^2 + 4x - 2)) + 1)/(-1(1(5x^2 + 4x - 2)) + 3)) + 2)/(-3((-2(1(5x^2 + 4x - 2)) + 1)/(-1(1(5x^2 + 4x - 2)) + 3)) - 3)) - 1)/(2((1((-2(1(5x^2 + 4x - 2)) + 1)/(-1(1(5x^2 + 4x - 2)) + 3)) + 2)/(-3((-2(1(5x^2 + 4x - 2)) + 1)/(-1(1(5x^2 + 4x - 2)) + 3)) - 3))) and g(x) = 1(5(3|(-2sin(3\u03c0x - 3) + 3)| - 1) - 3)^2 - 3(5(3|(-2sin(3\u03c0x - 3) + 3)| - 1) - 3) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 4(-3(1((-1((-2x - 3)/(3x - 2)) + 2)/(-1((-2x - 3)/(3x - 2)) + 3))^2 + 4((-1((-2x - 3)/(3x - 2)) + 2)/(-1((-2x - 3)/(3x - 2)) + 3)) - 3)^2 + 5(1((-1((-2x - 3)/(3x - 2)) + 2)/(-1((-2x - 3)/(3x - 2)) + 3))^2 + 4((-1((-2x - 3)/(3x - 2)) + 2)/(-1((-2x - 3)/(3x - 2)) + 3)) - 3) - 2)^2 - 1(-3(1((-1((-2x - 3)/(3x - 2)) + 2)/(-1((-2x - 3)/(3x - 2)) + 3))^2 + 4((-1((-2x - 3)/(3x - 2)) + 2)/(-1((-2x - 3)/(3x - 2)) + 3)) - 3)^2 + 5(1((-1((-2x - 3)/(3x - 2)) + 2)/(-1((-2x - 3)/(3x - 2)) + 3))^2 + 4((-1((-2x - 3)/(3x - 2)) + 2)/(-1((-2x - 3)/(3x - 2)) + 3)) - 3) - 2) - 5 and g(x) = (-1(1(-2|(5x - 1) + 1|)^2 - 5(-2|(5x - 1) + 1|) + 4) + 3)/(-1(1(-2|(5x - 1) + 1|)^2 - 5(-2|(5x - 1) + 1|) + 4)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1(-4((1(-1(1x + 1) - 3) - 1)/(1(-1(1x + 1) - 3) + 3))) + 1)/(-3(-4((1(-1(1x + 1) - 3) - 1)/(1(-1(1x + 1) - 3) + 3)))) and g(x) = (1(2|((-3(1e^(-1x) + 1) + 2)/(-1(1e^(-1x) + 1) - 2)) - 3| - 1) - 2)/(-2(2|((-3(1e^(-1x) + 1) + 2)/(-1(1e^(-1x) + 1) - 2)) - 3| - 1) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(1(4(-4((-2x + 2)/(-2x)) + 2)^2 - 1(-4((-2x + 2)/(-2x)) + 2) + 4) - 1) + 3)/(-1(1(4(-4((-2x + 2)/(-2x)) + 2)^2 - 1(-4((-2x + 2)/(-2x)) + 2) + 4) - 1) + 2) and g(x) = (2(2(-2(-3x + 2) - 4) - 1) + 2)/(3(2(-2(-3x + 2) - 4) - 1) + 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(-5((-3(3e^(2(4x + 1)) - 2) + 3)/(-1(3e^(2(4x + 1)) - 2) - 3))^2 - 5((-3(3e^(2(4x + 1)) - 2) + 3)/(-1(3e^(2(4x + 1)) - 2) - 3)) - 3))/(-1(-5((-3(3e^(2(4x + 1)) - 2) + 3)/(-1(3e^(2(4x + 1)) - 2) - 3))^2 - 5((-3(3e^(2(4x + 1)) - 2) + 3)/(-1(3e^(2(4x + 1)) - 2) - 3)) - 3) - 3) and g(x) = -2|(1(-1((2x + 1)/(2x + 3))^2 + 2((2x + 1)/(2x + 3)) - 4) + 2) + 3| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-2(1|(3((-2(2x^2 + 4x - 5) - 2)/(-2(2x^2 + 4x - 5) - 3)) + 3) + 3| + 3) + 1)/(-1(1|(3((-2(2x^2 + 4x - 5) - 2)/(-2(2x^2 + 4x - 5) - 3)) + 3) + 3| + 3) - 3) and g(x) = 1|(3((-2(-1x - 4) - 3)/(-3(-1x - 4))) + 5)| meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2(-1|((2((-3((1x - 3)/(3x - 2)))/(2((1x - 3)/(3x - 2)) + 3)) + 2)/(-2((-3((1x - 3)/(3x - 2)))/(2((1x - 3)/(3x - 2)) + 3)))) + 3| + 1)^2 + 4(-1|((2((-3((1x - 3)/(3x - 2)))/(2((1x - 3)/(3x - 2)) + 3)) + 2)/(-2((-3((1x - 3)/(3x - 2)))/(2((1x - 3)/(3x - 2)) + 3)))) + 3| + 1) - 2 and g(x) = -4(-1(-4(2x - 5) - 3)^2 + 4(-4(2x - 5) - 3) - 2)^2 + 1(-1(-4(2x - 5) - 3)^2 + 4(-4(2x - 5) - 3) - 2) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2((1(2|(-1|(-1|x| - 3) + 3|) - 1| - 2) - 3)/(3(2|(-1|(-1|x| - 3) + 3|) - 1| - 2) + 1))^2 + 1 and g(x) = (-1(-3cos(1\u03c0((-2(5x^2 - 3x + 2) - 1)/(3(5x^2 - 3x + 2))) - 1)) - 3)/(-2(-3cos(1\u03c0((-2(5x^2 - 3x + 2) - 1)/(3(5x^2 - 3x + 2))) - 1)) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -1(-5(-5((3((3x + 2)/(3x)) - 3)/(2((3x + 2)/(3x)))) + 1)^2 - 5(-5((3((3x + 2)/(3x)) - 3)/(2((3x + 2)/(3x)))) + 1) + 2)^2 + 1(-5(-5((3((3x + 2)/(3x)) - 3)/(2((3x + 2)/(3x)))) + 1)^2 - 5(-5((3((3x + 2)/(3x)) - 3)/(2((3x + 2)/(3x)))) + 1) + 2) - 4 and g(x) = (-1(5((-1(-3|x + 3| + 3) + 2)/(1(-3|x + 3| + 3) - 3))^2 + 2((-1(-3|x + 3| + 3) + 2)/(1(-3|x + 3| + 3) - 3)) - 1) - 2)/(2(5((-1(-3|x + 3| + 3) + 2)/(1(-3|x + 3| + 3) - 3))^2 + 2((-1(-3|x + 3| + 3) + 2)/(1(-3|x + 3| + 3) - 3)) - 1) - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -3|(3(1((3(2x + 2) - 1)/(3(2x + 2) - 2)))^2 + 1(1((3(2x + 2) - 1)/(3(2x + 2) - 2))) + 1) - 1| - 2 and g(x) = -1(-2|(3(-1|x + 2|)) - 2| - 3)^2 - 4(-2|(3(-1|x + 2|)) - 2| - 3) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1|((1((-2(5(-4x + 2) + 1) - 1)/(-1(5(-4x + 2) + 1))) + 1)/(3((-2(5(-4x + 2) + 1) - 1)/(-1(5(-4x + 2) + 1))) - 2)) + 3| - 3 and g(x) = 2|((3((3(5x^2 + 1x + 2) + 3)/(2(5x^2 + 1x + 2))) + 3)/(1((3(5x^2 + 1x + 2) + 3)/(2(5x^2 + 1x + 2))) + 3))| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-2((1(2((1(-1cos(2\u03c0x) + 2) - 2)/(-1(-1cos(2\u03c0x) + 2) - 3)) + 4) - 2)/(2(2((1(-1cos(2\u03c0x) + 2) - 2)/(-1(-1cos(2\u03c0x) + 2) - 3)) + 4) + 1)) + 2)/(-2((1(2((1(-1cos(2\u03c0x) + 2) - 2)/(-1(-1cos(2\u03c0x) + 2) - 3)) + 4) - 2)/(2(2((1(-1cos(2\u03c0x) + 2) - 2)/(-1(-1cos(2\u03c0x) + 2) - 3)) + 4) + 1)) - 1) and g(x) = (-3(1(3((-2x + 2)/(-2x + 3)) + 4)^2 + 5(3((-2x + 2)/(-2x + 3)) + 4) - 1))/(2(1(3((-2x + 2)/(-2x + 3)) + 4)^2 + 5(3((-2x + 2)/(-2x + 3)) + 4) - 1) + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 4(1(5(1(1x^2 - 3x - 1)^2 + 4(1x^2 - 3x - 1) - 1) + 2) - 3) - 2 and g(x) = 2(2(2(3x^2 - 4) + 4)^2 - 2(2(3x^2 - 4) + 4) + 1)^2 + 4(2(2(3x^2 - 4) + 4)^2 - 2(2(3x^2 - 4) + 4) + 1) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-1(3(-1e^(-1(1((-1x - 2)/(2x - 1)) - 3)) + 2) - 4) - 3)/(-2(3(-1e^(-1(1((-1x - 2)/(2x - 1)) - 3)) + 2) - 4) - 3) and g(x) = -2((-2(-3(-3|x - 2| - 1) - 5) - 1)/(1(-3(-3|x - 2| - 1) - 5))) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1((1(5((1((2x + 3)/(-2x - 2)) - 3)/(3((2x + 3)/(-2x - 2)) + 1)) + 4) + 3)/(-2(5((1((2x + 3)/(-2x - 2)) - 3)/(3((2x + 3)/(-2x - 2)) + 1)) + 4) - 2)) - 1 and g(x) = (-1(1cos(1\u03c0(2|(4x - 5) + 3| + 2) - 2) + 2) + 2)/(2(1cos(1\u03c0(2|(4x - 5) + 3| + 2) - 2) + 2) - 1) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 4(5(-1(-3e^(-2(-3x^2 - 4x)) - 2) - 2) - 2)^2 - 5(5(-1(-3e^(-2(-3x^2 - 4x)) - 2) - 2) - 2) + 1 and g(x) = 4(4(-1cos(1\u03c0(-1x + 2) + 2) + 3)^2 - 4(-1cos(1\u03c0(-1x + 2) + 2) + 3) - 3) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3|(3|(-1|(-3((-1x + 3)/(-1x - 2))^2 - 1((-1x + 3)/(-1x - 2)) + 1) - 2| + 3) - 2|) - 3| + 1 and g(x) = -4((-1(-1|((2x)/(2x - 1)) + 3|))/(-2(-1|((2x)/(2x - 1)) + 3|) - 1)) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1|(-3|(-4(-2|((-3x + 3)/(2x - 1)) - 3| - 3)^2 + 1(-2|((-3x + 3)/(2x - 1)) - 3| - 3) - 2) - 1| + 3) + 2| - 3 and g(x) = -4(2e^(-1(-2((-1x - 2)/(-2x - 3))^2 - 2((-1x - 2)/(-2x - 3)) + 1)) + 2) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -5(1|((1(1((3x - 2)/(-1x - 3))^2 - 2((3x - 2)/(-1x - 3)) + 1) - 3)/(-3(1((3x - 2)/(-1x - 3))^2 - 2((3x - 2)/(-1x - 3)) + 1) + 1)) + 3| - 1) - 3 and g(x) = 2|(-1((2(-4x - 4))/(2(-4x - 4) + 2))^2 + 2((2(-4x - 4))/(2(-4x - 4) + 2)) - 4) + 3| meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (2((-1(-4(-2|((1x - 3)/(-1x - 3)) - 1| - 3) + 1) + 3)/(-1(-4(-2|((1x - 3)/(-1x - 3)) - 1| - 3) + 1) - 1)))/(-1((-1(-4(-2|((1x - 3)/(-1x - 3)) - 1| - 3) + 1) + 3)/(-1(-4(-2|((1x - 3)/(-1x - 3)) - 1| - 3) + 1) - 1)) - 2) and g(x) = 1|(4(-2(-2x) + 5) + 4)| - 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3(4(-1|(5(-2|x| - 1)^2 - 4(-2|x| - 1) - 5) - 1| - 2)^2 - 1(-1|(5(-2|x| - 1)^2 - 4(-2|x| - 1) - 5) - 1| - 2) + 5) - 4 and g(x) = 3|((3(1((1x - 3)/(-2x - 1)) - 5) - 2)/(1(1((1x - 3)/(-2x - 1)) - 5))) - 1| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1(-1(4((1(3x + 3) - 3)/(1(3x + 3) + 2))^2 - 1((1(3x + 3) - 3)/(1(3x + 3) + 2)) + 4)^2 + 1(4((1(3x + 3) - 3)/(1(3x + 3) + 2))^2 - 1((1(3x + 3) - 3)/(1(3x + 3) + 2)) + 4) + 5) + 4 and g(x) = -1(-5(-1(-1x^2 + 1x - 1)^2 - 2(-1x^2 + 1x - 1) + 4) - 5) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1((-1(2((-2(-3e^(-1x)) - 1)/(-1(-3e^(-1x)) + 2))^2 - 4((-2(-3e^(-1x)) - 1)/(-1(-3e^(-1x)) + 2))) + 3)/(2(2((-2(-3e^(-1x)) - 1)/(-1(-3e^(-1x)) + 2))^2 - 4((-2(-3e^(-1x)) - 1)/(-1(-3e^(-1x)) + 2))) - 3)) + 1 and g(x) = (1(-5(-1(1x^2 - 2x + 1)^2 + 1(1x^2 - 2x + 1) + 5)) - 1)/(-1(-5(-1(1x^2 - 2x + 1)^2 + 1(1x^2 - 2x + 1) + 5)) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-1(5(2(3|(1|x - 3| + 1)| - 2) + 5)^2 - 5(2(3|(1|x - 3| + 1)| - 2) + 5) + 3) + 2)/(-1(5(2(3|(1|x - 3| + 1)| - 2) + 5)^2 - 5(2(3|(1|x - 3| + 1)| - 2) + 5) + 3) - 2) and g(x) = (2((-2(-5(-3x - 2) + 1) - 1)/(2(-5(-3x - 2) + 1) - 1)) + 2)/(-1((-2(-5(-3x - 2) + 1) - 1)/(2(-5(-3x - 2) + 1) - 1))) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 2|((-1(3|((3((1x + 3)/(-1x + 2)) - 1)/(-2((1x + 3)/(-1x + 2)) + 3)) - 2| + 3) + 2)/(3(3|((3((1x + 3)/(-1x + 2)) - 1)/(-2((1x + 3)/(-1x + 2)) + 3)) - 2| + 3) - 1)) - 3| + 3 and g(x) = 4((-3(1|(1|x - 1| + 3) - 2| - 1) + 3)/(2(1|(1|x - 1| + 3) - 2| - 1) - 3)) - 4 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (2((3(-5(4(4x^2 + 5x)^2 - 2(4x^2 + 5x) + 1)^2 - 4(4(4x^2 + 5x)^2 - 2(4x^2 + 5x) + 1) + 4) - 1)/(-3(-5(4(4x^2 + 5x)^2 - 2(4x^2 + 5x) + 1)^2 - 4(4(4x^2 + 5x)^2 - 2(4x^2 + 5x) + 1) + 4) - 2)))/(-3((3(-5(4(4x^2 + 5x)^2 - 2(4x^2 + 5x) + 1)^2 - 4(4(4x^2 + 5x)^2 - 2(4x^2 + 5x) + 1) + 4) - 1)/(-3(-5(4(4x^2 + 5x)^2 - 2(4x^2 + 5x) + 1)^2 - 4(4(4x^2 + 5x)^2 - 2(4x^2 + 5x) + 1) + 4) - 2))) and g(x) = -3(-1|((1((2x - 2)/(-2x + 3)))/(1((2x - 2)/(-2x + 3)) - 3)) + 3| + 2) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (3(2sin(2\u03c0(-2|(1(1x + 2)^2 - 2(1x + 2) + 2) + 3| - 2) - 2) - 1) - 1)/(1(2sin(2\u03c0(-2|(1(1x + 2)^2 - 2(1x + 2) + 2) + 3| - 2) - 2) - 1) - 2) and g(x) = 2|((2(-4(-5x^2 + 2x + 5)^2 + 4(-5x^2 + 2x + 5) + 5) - 3)/(-1(-4(-5x^2 + 2x + 5)^2 + 4(-5x^2 + 2x + 5) + 5))) - 3| - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1(-4(-1(-3e^(-2(1x^2 + 2x + 3)) + 1)^2 - 1(-3e^(-2(1x^2 + 2x + 3)) + 1) - 5) - 1)^2 - 4(-4(-1(-3e^(-2(1x^2 + 2x + 3)) + 1)^2 - 1(-3e^(-2(1x^2 + 2x + 3)) + 1) - 5) - 1) and g(x) = (2(1|((-3((-3x + 1)/(2x - 3)))/(-2((-3x + 1)/(2x - 3)) + 1)) + 1| - 1) + 3)/(2(1|((-3((-3x + 1)/(2x - 3)))/(-2((-3x + 1)/(2x - 3)) + 1)) + 1| - 1) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3|(2sin(1\u03c0(-3((-3(1x - 1) - 1)/(1(1x - 1) + 1)) - 2) - 2))| and g(x) = -1|(-3(2(-1x + 4) + 5)^2 + 1(2(-1x + 4) + 5)) - 3| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(1(2((3(5x - 2) - 3)/(-2(5x - 2) - 1))^2 + 4((3(5x - 2) - 3)/(-2(5x - 2) - 1))) - 4) + 1)/(3(1(2((3(5x - 2) - 3)/(-2(5x - 2) - 1))^2 + 4((3(5x - 2) - 3)/(-2(5x - 2) - 1))) - 4) + 3) and g(x) = 1|(3cos(3\u03c0(3(-3x^2 + 3x + 5)^2 - 4(-3x^2 + 3x + 5)) - 2) - 3) - 1| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (3((1(1|(-3|(3x^2 - 4x + 3) + 2|) - 1| - 2) + 2)/(-2(1|(-3|(3x^2 - 4x + 3) + 2|) - 1| - 2) - 1)) + 3)/(-2((1(1|(-3|(3x^2 - 4x + 3) + 2|) - 1| - 2) + 2)/(-2(1|(-3|(3x^2 - 4x + 3) + 2|) - 1| - 2) - 1)) + 3) and g(x) = (1(-5(-4((1x - 2)/(3x - 1)) + 1)^2 - 3(-4((1x - 2)/(3x - 1)) + 1) + 1) + 3)/(2(-5(-4((1x - 2)/(3x - 1)) + 1)^2 - 3(-4((1x - 2)/(3x - 1)) + 1) + 1) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-3(4(1(-1e^(1(4x - 1)) + 3)^2 + 2(-1e^(1(4x - 1)) + 3) - 2) + 1) + 3)/(-3(4(1(-1e^(1(4x - 1)) + 3)^2 + 2(-1e^(1(4x - 1)) + 3) - 2) + 1) + 2) and g(x) = (2(-3e^(2(2|((-1x)/(1x + 3)) - 1| - 3)) + 3) - 3)/(-1(-3e^(2(2|((-1x)/(1x + 3)) - 1| - 3)) + 3) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(-3((2(-2e^(1(-4x^2 - 2x - 1)) - 1))/(-3(-2e^(1(-4x^2 - 2x - 1)) - 1) - 1))^2 + 1((2(-2e^(1(-4x^2 - 2x - 1)) - 1))/(-3(-2e^(1(-4x^2 - 2x - 1)) - 1) - 1))) - 2)/(3(-3((2(-2e^(1(-4x^2 - 2x - 1)) - 1))/(-3(-2e^(1(-4x^2 - 2x - 1)) - 1) - 1))^2 + 1((2(-2e^(1(-4x^2 - 2x - 1)) - 1))/(-3(-2e^(1(-4x^2 - 2x - 1)) - 1) - 1))) - 2) and g(x) = -2|(1|(-3e^(-2(5x^2 + 3x - 4)) - 1) - 2| - 3) - 1| + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 5(-2|(-2((-1(-3x) + 1)/(2(-3x)))^2 - 5) - 2| - 3) + 2 and g(x) = -3(5(1|(3e^(1x) + 3) - 2|) - 4)^2 + 5(5(1|(3e^(1x) + 3) - 2|) - 4) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (3(2cos(3\u03c0(-4((3(5x - 5) - 1)/(3(5x - 5) + 1))^2 - 4((3(5x - 5) - 1)/(3(5x - 5) + 1)) - 2) - 1) + 3) + 3)/(-2(2cos(3\u03c0(-4((3(5x - 5) - 1)/(3(5x - 5) + 1))^2 - 4((3(5x - 5) - 1)/(3(5x - 5) + 1)) - 2) - 1) + 3) + 3) and g(x) = (1((3(5(-1x + 2) - 3) + 3)/(1(5(-1x + 2) - 3))) + 2)/(1((3(5(-1x + 2) - 3) + 3)/(1(5(-1x + 2) - 3)))) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2(-1e^(-1((1(-2(-4x^2 + 5x - 4)) + 2)/(1(-2(-4x^2 + 5x - 4)) - 3))) - 2) - 4 and g(x) = (1(-5((-3(-1x^2 - 5x - 4) - 3)/(-1(-1x^2 - 5x - 4))) - 4) + 2)/(-2(-5((-3(-1x^2 - 5x - 4) - 3)/(-1(-1x^2 - 5x - 4))) - 4) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2|((-1(3e^(-1(1((1x + 2)/(-3x - 3)) + 2)) + 2) - 2)/(3(3e^(-1(1((1x + 2)/(-3x - 3)) + 2)) + 2))) + 1| + 1 and g(x) = (-3(-4(-3(-2x) - 1)^2 - 2(-3(-2x) - 1) + 5) - 2)/(2(-4(-3(-2x) - 1)^2 - 2(-3(-2x) - 1) + 5) - 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3|((3(-1(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 4) - 1)/(-3(-1(-4(-1sin(1\u03c0x + 3) - 2) + 1) + 4))) - 3| - 1 and g(x) = (2((2(-4(2x + 5)^2 - 2(2x + 5) + 5) - 1)/(2(-4(2x + 5)^2 - 2(2x + 5) + 5))) + 3)/(-2((2(-4(2x + 5)^2 - 2(2x + 5) + 5) - 1)/(2(-4(2x + 5)^2 - 2(2x + 5) + 5))) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-2(3((2((2((1x)/(1x + 3)) + 2)/(-1((1x)/(1x + 3)))))/(-3((2((1x)/(1x + 3)) + 2)/(-1((1x)/(1x + 3)))) - 3)) + 3) - 3)/(-1(3((2((2((1x)/(1x + 3)) + 2)/(-1((1x)/(1x + 3)))))/(-3((2((1x)/(1x + 3)) + 2)/(-1((1x)/(1x + 3)))) - 3)) + 3) - 3) and g(x) = -1|(-1|(2(2x - 1)^2 - 2(2x - 1) - 2) - 2| - 2) - 2| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 5(1|(-5(1|(-3x + 2) - 2| + 1) + 3) - 2| + 2) - 5 and g(x) = 3(-1|(-4(-3x + 5)^2 + 2(-3x + 5) + 4) - 1| - 2)^2 - 3(-1|(-4(-3x + 5)^2 + 2(-3x + 5) + 4) - 1| - 2) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1((-3((1((-1(1x^2 + 3x - 2) + 2)/(1(1x^2 + 3x - 2) + 3)) - 2)/(-1((-1(1x^2 + 3x - 2) + 2)/(1(1x^2 + 3x - 2) + 3)))) - 1)/(1((1((-1(1x^2 + 3x - 2) + 2)/(1(1x^2 + 3x - 2) + 3)) - 2)/(-1((-1(1x^2 + 3x - 2) + 2)/(1(1x^2 + 3x - 2) + 3)))) + 1)) - 2)/(3((-3((1((-1(1x^2 + 3x - 2) + 2)/(1(1x^2 + 3x - 2) + 3)) - 2)/(-1((-1(1x^2 + 3x - 2) + 2)/(1(1x^2 + 3x - 2) + 3)))) - 1)/(1((1((-1(1x^2 + 3x - 2) + 2)/(1(1x^2 + 3x - 2) + 3)) - 2)/(-1((-1(1x^2 + 3x - 2) + 2)/(1(1x^2 + 3x - 2) + 3)))) + 1)) - 1) and g(x) = (2(3(-4(2x^2 + 1x - 5) - 2) - 5))/(1(3(-4(2x^2 + 1x - 5) - 2) - 5)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1(-1|((1(1(-3x)^2 + 5(-3x) - 2) - 1)/(2(1(-3x)^2 + 5(-3x) - 2) + 1)) + 1| - 1) + 1 and g(x) = -1|(-5(-3|(2|x + 1| - 2) - 2| - 1) + 4) + 2| + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1|((-2(1(1(2x + 4) - 4)))/(2(1(1(2x + 4) - 4)) + 2)) + 1| - 2 and g(x) = 1|(5(-4((-1x + 1)/(-3x + 1))^2 + 1((-1x + 1)/(-3x + 1)) - 2) + 1) + 1| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-1(-5(-1(3(-2x^2 - 1x + 5) + 5) - 2)^2 - 3(-1(3(-2x^2 - 1x + 5) + 5) - 2) + 2) + 2)/(3(-5(-1(3(-2x^2 - 1x + 5) + 5) - 2)^2 - 3(-1(3(-2x^2 - 1x + 5) + 5) - 2) + 2) - 2) and g(x) = 2(-2|((-3(-3x) + 3)/(-1(-3x) - 1)) + 2|) + 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 4((1((-2((1(-3x + 1) + 2)/(2(-3x + 1) + 1)) + 2)/(1((1(-3x + 1) + 2)/(2(-3x + 1) + 1)) + 2)) + 1)/(3((-2((1(-3x + 1) + 2)/(2(-3x + 1) + 1)) + 2)/(1((1(-3x + 1) + 2)/(2(-3x + 1) + 1)) + 2)) - 1))^2 - 4((1((-2((1(-3x + 1) + 2)/(2(-3x + 1) + 1)) + 2)/(1((1(-3x + 1) + 2)/(2(-3x + 1) + 1)) + 2)) + 1)/(3((-2((1(-3x + 1) + 2)/(2(-3x + 1) + 1)) + 2)/(1((1(-3x + 1) + 2)/(2(-3x + 1) + 1)) + 2)) - 1)) - 3 and g(x) = (-1(1|(3(2x^2 - 1x + 2) + 1) + 3| - 3) - 3)/(2(1|(3(2x^2 - 1x + 2) + 1) + 3| - 3) + 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1((-2((-3(2(-4x) - 2) + 2)/(1(2(-4x) - 2) - 3)) - 3)/(-1((-3(2(-4x) - 2) + 2)/(1(2(-4x) - 2) - 3)) - 3)) - 4 and g(x) = 1cos(1\u03c0((-2(-1(-2|x - 1| + 3)^2 - 2(-2|x - 1| + 3) - 2) - 2)/(1(-1(-2|x - 1| + 3)^2 - 2(-2|x - 1| + 3) - 2))) - 1) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3(-2(-1(-3(1x - 5) + 5) - 1))^2 - 5(-2(-1(-3(1x - 5) + 5) - 1)) - 1 and g(x) = (-3((2(-5((3x - 3)/(-1x - 1))^2 - 4((3x - 3)/(-1x - 1))) - 2)/(-3(-5((3x - 3)/(-1x - 1))^2 - 4((3x - 3)/(-1x - 1))) + 2)) + 1)/(-1((2(-5((3x - 3)/(-1x - 1))^2 - 4((3x - 3)/(-1x - 1))) - 2)/(-3(-5((3x - 3)/(-1x - 1))^2 - 4((3x - 3)/(-1x - 1))) + 2)) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (1((3((1(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 3)/(-1(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 2)) - 3)/(2((1(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 3)/(-1(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 2)) + 2)) - 3)/(-2((3((1(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 3)/(-1(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 2)) - 3)/(2((1(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 3)/(-1(1(-2|x + 1| - 3)^2 + 4(-2|x + 1| - 3) + 5) - 2)) + 2)) - 3) and g(x) = 2|(2|(4(1x)^2 + 2(1x) - 3) + 2| + 1) - 2| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|(-2(4(-2(-3x + 3) - 1)^2 - 4(-2(-3x + 3) - 1) - 1) - 5) - 1| + 3 and g(x) = 2(-2sin(1\u03c0(2(-3x^2 + 4) + 3)) + 3) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(-1(4(1|(-1cos(3\u03c0x) + 3) + 2| - 3)^2 - 3(1|(-1cos(3\u03c0x) + 3) + 2| - 3) + 5)^2 - 2(4(1|(-1cos(3\u03c0x) + 3) + 2| - 3)^2 - 3(1|(-1cos(3\u03c0x) + 3) + 2| - 3) + 5) + 4))/(-3(-1(4(1|(-1cos(3\u03c0x) + 3) + 2| - 3)^2 - 3(1|(-1cos(3\u03c0x) + 3) + 2| - 3) + 5)^2 - 2(4(1|(-1cos(3\u03c0x) + 3) + 2| - 3)^2 - 3(1|(-1cos(3\u03c0x) + 3) + 2| - 3) + 5) + 4) - 1) and g(x) = -1|(-4((-2(2x - 4) - 1)/(3(2x - 4) + 3)) - 2) - 1| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1(-1e^(-1(-2(4(1x + 1) - 1) + 1))) - 4 and g(x) = 4(-5(-4((-1x)/(1x + 3))) + 3)^2 - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (3(-1|((-3((-1((1x + 1)/(1x)) - 2)/(2((1x + 1)/(1x)) + 3)) - 2)/(-2((-1((1x + 1)/(1x)) - 2)/(2((1x + 1)/(1x)) + 3)) - 3)) + 2| + 3) - 2)/(-2(-1|((-3((-1((1x + 1)/(1x)) - 2)/(2((1x + 1)/(1x)) + 3)) - 2)/(-2((-1((1x + 1)/(1x)) - 2)/(2((1x + 1)/(1x)) + 3)) - 3)) + 2| + 3) + 3) and g(x) = -1|(-2e^(1(-5((-3x + 3)/(-2x - 1))^2 + 4((-3x + 3)/(-2x - 1)) + 5)) - 3) + 3| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1|((2(-3cos(3\u03c0(1(-1x + 3)^2 - 3(-1x + 3) - 4) + 1) + 2) + 3)/(2(-3cos(3\u03c0(1(-1x + 3)^2 - 3(-1x + 3) - 4) + 1) + 2) + 3))| and g(x) = 2e^(-1((-3((3((-3x - 3)/(2x + 3)) + 1)/(2((-3x - 3)/(2x + 3)) + 1)) - 2)/(-2((3((-3x - 3)/(2x + 3)) + 1)/(2((-3x - 3)/(2x + 3)) + 1)) - 1))) - 1 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1|((-1(3(-2(-1x - 2)^2 - 4(-1x - 2) + 2) - 3) + 2)/(3(3(-2(-1x - 2)^2 - 4(-1x - 2) + 2) - 3) - 2)) - 2| + 3 and g(x) = -1(3(3|(-3|x - 1| - 1) + 3|)^2 - 1(3|(-3|x - 1| - 1) + 3|) + 1) - 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-1((-1(1|((1(-1|x + 3| + 1) + 2)/(1(-1|x + 3| + 1) + 3)) - 2| - 2) - 1)/(2(1|((1(-1|x + 3| + 1) + 2)/(1(-1|x + 3| + 1) + 3)) - 2| - 2) + 3)) - 2)/(-1((-1(1|((1(-1|x + 3| + 1) + 2)/(1(-1|x + 3| + 1) + 3)) - 2| - 2) - 1)/(2(1|((1(-1|x + 3| + 1) + 2)/(1(-1|x + 3| + 1) + 3)) - 2| - 2) + 3)) - 1) and g(x) = -3(2(4(4x - 3)^2 + 4(4x - 3) - 5) - 3) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 5(-2|(4((-2(1|x + 1| - 2) + 2)/(-1(1|x + 1| - 2) + 3))^2 - 3((-2(1|x + 1| - 2) + 2)/(-1(1|x + 1| - 2) + 3)) + 1)| - 2) and g(x) = -5(3e^(1(1(-4x - 3)^2 + 1(-4x - 3) - 1)) + 2) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1|(1|(1(-4(-3|x + 3| + 1) + 1)^2 + 5) - 3| - 1) + 1| - 1 and g(x) = -1sin(3\u03c0(3|(-2|(3x^2 - 1x + 1) - 2| + 2)| + 2) + 2) - 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(1((-2(2((2x + 3)/(-2x - 3)) - 2) - 3)/(2(2((2x + 3)/(-2x - 3)) - 2) - 1)) + 4) - 3)/(2(1((-2(2((2x + 3)/(-2x - 3)) - 2) - 3)/(2(2((2x + 3)/(-2x - 3)) - 2) - 1)) + 4)) and g(x) = -5(-3e^(-1(5(2x^2 - 4x - 2) - 1)) - 1)^2 - 5(-3e^(-1(5(2x^2 - 4x - 2) - 1)) - 1) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(-2|(-2((-1(3x^2 + 2x - 4) + 2)/(-1(3x^2 + 2x - 4) + 2)) - 2) + 3| + 2) - 3)/(3(-2|(-2((-1(3x^2 + 2x - 4) + 2)/(-1(3x^2 + 2x - 4) + 2)) - 2) + 3| + 2) + 2) and g(x) = -1(2(1(-2e^(2x) + 3) - 4) + 1) - 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2(-3((3(5(2|x + 1| - 1) + 4) + 3)/(2(5(2|x + 1| - 1) + 4)))^2 + 5((3(5(2|x + 1| - 1) + 4) + 3)/(2(5(2|x + 1| - 1) + 4))) - 1) - 2)/(1(-3((3(5(2|x + 1| - 1) + 4) + 3)/(2(5(2|x + 1| - 1) + 4)))^2 + 5((3(5(2|x + 1| - 1) + 4) + 3)/(2(5(2|x + 1| - 1) + 4))) - 1)) and g(x) = 1|((-2(-1|(2e^(-2x) + 3)| + 3) + 2)/(2(-1|(2e^(-2x) + 3)| + 3))) + 1| - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5(1((-2(5((1x - 2)/(-1x - 3))^2 - 4((1x - 2)/(-1x - 3)) - 5) - 3)/(2(5((1x - 2)/(-1x - 3))^2 - 4((1x - 2)/(-1x - 3)) - 5) + 1))^2 + 2((-2(5((1x - 2)/(-1x - 3))^2 - 4((1x - 2)/(-1x - 3)) - 5) - 3)/(2(5((1x - 2)/(-1x - 3))^2 - 4((1x - 2)/(-1x - 3)) - 5) + 1)) - 3) + 2 and g(x) = -4(2|((-3(1x + 1) + 1)/(2(1x + 1) + 2)) - 3| - 3)^2 - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2(-1|(1(1|(1|x + 1|)| - 1)^2 + 5(1|(1|x + 1|)| - 1) + 1) - 2|)^2 - 3(-1|(1(1|(1|x + 1|)| - 1)^2 + 5(1|(1|x + 1|)| - 1) + 1) - 2|) + 4 and g(x) = 4(3(-5(3|x + 3| - 1) + 1))^2 - 5(3(-5(3|x + 3| - 1) + 1)) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 5(1|(-3|(3((1x + 2)/(-2x)) + 4) + 3| + 1) - 3|)^2 - 5(1|(-3|(3((1x + 2)/(-2x)) + 4) + 3| + 1) - 3|) + 5 and g(x) = 3|(-4(5(-4x + 1)^2 + 1(-4x + 1) + 1)^2 - 4(5(-4x + 1)^2 + 1(-4x + 1) + 1) + 2)| + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-2(-1|(1((-3(-2x) - 3)/(1(-2x) + 3))^2 + 3((-3(-2x) - 3)/(1(-2x) + 3)) - 5) - 3| + 1) + 1)/(-1(-1|(1((-3(-2x) - 3)/(1(-2x) + 3))^2 + 3((-3(-2x) - 3)/(1(-2x) + 3)) - 5) - 3| + 1) - 3) and g(x) = (2((1(1(-3x) - 3) - 2)/(3(1(-3x) - 3) + 2)))/(-3((1(1(-3x) - 3) - 2)/(3(1(-3x) - 3) + 2)) + 4) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 5((-2((2(1((2x - 2)/(2x - 3))^2 + 4((2x - 2)/(2x - 3))) + 2)/(3(1((2x - 2)/(2x - 3))^2 + 4((2x - 2)/(2x - 3))))) - 1)/(2((2(1((2x - 2)/(2x - 3))^2 + 4((2x - 2)/(2x - 3))) + 2)/(3(1((2x - 2)/(2x - 3))^2 + 4((2x - 2)/(2x - 3))))) - 3))^2 + 4((-2((2(1((2x - 2)/(2x - 3))^2 + 4((2x - 2)/(2x - 3))) + 2)/(3(1((2x - 2)/(2x - 3))^2 + 4((2x - 2)/(2x - 3))))) - 1)/(2((2(1((2x - 2)/(2x - 3))^2 + 4((2x - 2)/(2x - 3))) + 2)/(3(1((2x - 2)/(2x - 3))^2 + 4((2x - 2)/(2x - 3))))) - 3)) + 1 and g(x) = -5(4(3(-1x^2 + 3x + 3) + 4) + 5) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2((-2(1|((-3(5x + 3) + 3)/(-1(5x + 3) - 2)) + 1| + 2) - 3)/(3(1|((-3(5x + 3) + 3)/(-1(5x + 3) - 2)) + 1| + 2) + 1)) + 4 and g(x) = (3(-5(-3|(-3x^2 - 4x + 3) - 1| + 3) - 4) + 1)/(3(-5(-3|(-3x^2 - 4x + 3) - 1| + 3) - 4) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -2(-3|(4(-1|((-3x + 2)/(2x - 1)) + 3| + 2) + 3)| + 2)^2 + 5(-3|(4(-1|((-3x + 2)/(2x - 1)) + 3| + 2) + 3)| + 2) and g(x) = -1(-1(-1sin(2\u03c0(-4x^2 + 1x - 3) - 3) - 3) + 4) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 1(-3|(-2|(2|(3|x - 1|) - 2| - 1) + 2| + 3) - 3| + 3) - 1 and g(x) = -5(1((-1(3|x|))/(1(3|x|) + 3))^2 - 3((-1(3|x|))/(1(3|x|) + 3))) + 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -4(3(2(5(2x - 1) - 2) - 2) - 5) - 2 and g(x) = 3(3e^(1(1(-4x - 2) - 4)) + 2)^2 - 3(3e^(1(1(-4x - 2) - 4)) + 2) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(-1(-1|(-2e^(1(-5x + 2)) + 1) - 2| - 1) - 4)^2 and g(x) = -2(-1(1(-4x^2 + 5x - 4)^2 + 3(-4x^2 + 5x - 4) + 3)^2 + 1(1(-4x^2 + 5x - 4)^2 + 3(-4x^2 + 5x - 4) + 3) + 1)^2 + 2(-1(1(-4x^2 + 5x - 4)^2 + 3(-4x^2 + 5x - 4) + 3)^2 + 1(1(-4x^2 + 5x - 4)^2 + 3(-4x^2 + 5x - 4) + 3) + 1) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(3(-2(1sin(2\u03c0(4x + 5) + 2) + 1) - 5)^2 - 3(-2(1sin(2\u03c0(4x + 5) + 2) + 1) - 5) - 3)^2 + 5(3(-2(1sin(2\u03c0(4x + 5) + 2) + 1) - 5)^2 - 3(-2(1sin(2\u03c0(4x + 5) + 2) + 1) - 5) - 3) + 3 and g(x) = (3(2|(1(-2cos(3\u03c0x - 1) - 2)^2 + 4(-2cos(3\u03c0x - 1) - 2) + 3) + 2| - 2) - 2)/(-3(2|(1(-2cos(3\u03c0x - 1) - 2)^2 + 4(-2cos(3\u03c0x - 1) - 2) + 3) + 2| - 2)) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4(3(-5(-3((3x + 2)/(3x + 3)) - 2)^2 + 1(-3((3x + 2)/(3x + 3)) - 2) + 2) - 5)^2 + 5(3(-5(-3((3x + 2)/(3x + 3)) - 2)^2 + 1(-3((3x + 2)/(3x + 3)) - 2) + 2) - 5) + 4 and g(x) = 2(-3|(3|((-3x - 1)/(2x - 3)) + 2| + 1) + 1| - 1) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2|(-2e^(2(1|(1((2x - 3)/(-2x))^2 - 2((2x - 3)/(-2x)) - 3) + 1| - 3)) + 3) + 3| - 1 and g(x) = -4(2cos(2\u03c0((3(1x + 4) + 1)/(-3(1x + 4) + 1)) - 1) - 1)^2 - 5(2cos(2\u03c0((3(1x + 4) + 1)/(-3(1x + 4) + 1)) - 1) - 1) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (3(2(4(-2((1x - 3)/(-1x - 2)) + 1)^2 + 2(-2((1x - 3)/(-1x - 2)) + 1))) + 3)/(-1(2(4(-2((1x - 3)/(-1x - 2)) + 1)^2 + 2(-2((1x - 3)/(-1x - 2)) + 1))) - 1) and g(x) = (3(-2(-5(-1x^2 - 3x + 1)) - 2) + 1)/(1(-2(-5(-1x^2 - 3x + 1)) - 2) - 2) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2((-2((-2((1(-2|x - 1| + 2) + 2)/(-1(-2|x - 1| + 2) - 1)) + 1)/(2((1(-2|x - 1| + 2) + 2)/(-1(-2|x - 1| + 2) - 1)) + 1)))/(3((-2((1(-2|x - 1| + 2) + 2)/(-1(-2|x - 1| + 2) - 1)) + 1)/(2((1(-2|x - 1| + 2) + 2)/(-1(-2|x - 1| + 2) - 1)) + 1)) + 1)) + 1 and g(x) = (1(3(-1(1x + 2) + 3)^2 + 1(-1(1x + 2) + 3) + 3) + 1)/(-2(3(-1(1x + 2) + 3)^2 + 1(-1(1x + 2) + 3) + 3) + 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -5(-5(1(5(-3x - 4) + 2) - 3)^2 + 3(1(5(-3x - 4) + 2) - 3) + 5)^2 - 4(-5(1(5(-3x - 4) + 2) - 3)^2 + 3(1(5(-3x - 4) + 2) - 3) + 5) - 3 and g(x) = -1((3(-2cos(1\u03c0((-3x + 3)/(2x + 1)) - 1) - 2))/(-1(-2cos(1\u03c0((-3x + 3)/(2x + 1)) - 1) - 2) - 3)) + 5 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (1(-5((1(1|(-4x^2 + 3x + 5)| - 1))/(3(1|(-4x^2 + 3x + 5)| - 1) - 1)) + 4) + 3)/(-3(-5((1(1|(-4x^2 + 3x + 5)| - 1))/(3(1|(-4x^2 + 3x + 5)| - 1) - 1)) + 4) + 2) and g(x) = -1|(2|(-1sin(1\u03c0((-3x - 1)/(-2x)) + 1) - 3)| + 3) - 1| - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -2|(2e^(-2(2(-1(2|x - 3| - 1)^2 - 5(2|x - 3| - 1) + 5) - 2)) + 1) - 1| + 2 and g(x) = 1sin(3\u03c0((2(-1|(-2x + 1) - 1| + 2) - 3)/(2(-1|(-2x + 1) - 1| + 2))) - 1) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 5((3(-3|(3(-4x^2 - 1x - 4)^2 - 4(-4x^2 - 1x - 4) - 5)| - 2) + 1)/(-3(-3|(3(-4x^2 - 1x - 4)^2 - 4(-4x^2 - 1x - 4) - 5)| - 2) + 1))^2 - 1((3(-3|(3(-4x^2 - 1x - 4)^2 - 4(-4x^2 - 1x - 4) - 5)| - 2) + 1)/(-3(-3|(3(-4x^2 - 1x - 4)^2 - 4(-4x^2 - 1x - 4) - 5)| - 2) + 1)) + 2 and g(x) = 1e^(1((2((1((-2x + 2)/(-1x + 3)))/(2((-2x + 2)/(-1x + 3)) + 3)))/(2((1((-2x + 2)/(-1x + 3)))/(2((-2x + 2)/(-1x + 3)) + 3)) - 1))) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(4(-1(1|(1x + 5) - 2| + 1) + 2) - 4)^2 + 4(4(-1(1|(1x + 5) - 2| + 1) + 2) - 4) + 4 and g(x) = (-1(-3|(-2|(1e^(1x) - 1) + 2| + 3) - 1| - 3) - 1)/(3(-3|(-2|(1e^(1x) - 1) + 2| + 3) - 1| - 3) - 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3(-3|(1(2(-4x - 3) - 4) + 3) + 3| + 1) - 4 and g(x) = -4((-2(-3(-1x^2 - 4x)^2 + 1(-1x^2 - 4x) + 2) + 3)/(2(-3(-1x^2 - 4x)^2 + 1(-1x^2 - 4x) + 2))) - 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 5(-5(-2|(-2|(-3|x + 2| + 2) - 2| + 2) - 2|)^2 - 4(-2|(-2|(-3|x + 2| + 2) - 2| + 2) - 2|) - 1)^2 - 5(-5(-2|(-2|(-3|x + 2| + 2) - 2| + 2) - 2|)^2 - 4(-2|(-2|(-3|x + 2| + 2) - 2| + 2) - 2|) - 1) + 4 and g(x) = 2|(4(5(5x^2 - 4x)^2 - 4(5x^2 - 4x) + 4) + 1) - 2| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -2|((2(5(2sin(1\u03c0(1x - 4) - 1) + 2)^2 + 4(2sin(1\u03c0(1x - 4) - 1) + 2)) + 2)/(2(5(2sin(1\u03c0(1x - 4) - 1) + 2)^2 + 4(2sin(1\u03c0(1x - 4) - 1) + 2)) + 3)) + 2| + 3 and g(x) = 3(-1|(5((3x + 2)/(3x + 1)) - 5) - 1| + 2) - 4 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3(5(4(-5((-2x + 3)/(-2x)) + 1))^2 - 4(4(-5((-2x + 3)/(-2x)) + 1)) - 4) - 4 and g(x) = 5(4((1(1x) - 1)/(-2(1x) - 2))^2 + 3((1(1x) - 1)/(-2(1x) - 2)) - 4) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2|((-2(1|(-2(-3e^(-1x) + 2)^2 - 1(-3e^(-1x) + 2)) - 2| - 2) - 2)/(3(1|(-2(-3e^(-1x) + 2)^2 - 1(-3e^(-1x) + 2)) - 2| - 2) - 1)) - 1| - 3 and g(x) = (-1(-1|(-3(-3cos(1\u03c0x + 3)) + 2) - 3| - 2) - 3)/(3(-1|(-3(-3cos(1\u03c0x + 3)) + 2) - 3| - 2) - 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -4(-2|((-2(3((2x - 2)/(1x + 3)) + 5) + 3)/(-2(3((2x - 2)/(1x + 3)) + 5) - 1)) + 3| - 1)^2 - 1(-2|((-2(3((2x - 2)/(1x + 3)) + 5) + 3)/(-2(3((2x - 2)/(1x + 3)) + 5) - 1)) + 3| - 1) + 5 and g(x) = 1cos(2\u03c0(5((1(2|x + 2| + 2) - 3)/(-1(2|x + 2| + 2) + 2)) - 1) - 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (3(3|(3sin(1\u03c0(4(1x^2 - 2x - 4) - 4) + 3)) - 1|) + 3)/(-3(3|(3sin(1\u03c0(4(1x^2 - 2x - 4) - 4) + 3)) - 1|) + 2) and g(x) = -4(-3(2cos(1\u03c0(5x^2 - 4x - 1) + 3) - 3)^2 + 3(2cos(1\u03c0(5x^2 - 4x - 1) + 3) - 3) + 1)^2 - 3(-3(2cos(1\u03c0(5x^2 - 4x - 1) + 3) - 3)^2 + 3(2cos(1\u03c0(5x^2 - 4x - 1) + 3) - 3) + 1) - 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-3(2|(5(3|(5x^2 + 5x) - 3| + 2) - 1) + 3| + 3) + 2)/(2(2|(5(3|(5x^2 + 5x) - 3| + 2) - 1) + 3| + 3) - 3) and g(x) = (1((2(-3((-2x + 2)/(-1x - 3)) + 1))/(2(-3((-2x + 2)/(-1x - 3)) + 1) + 2)) - 3)/(3((2(-3((-2x + 2)/(-1x - 3)) + 1))/(2(-3((-2x + 2)/(-1x - 3)) + 1) + 2)) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -2(1(-3((2(2x + 5) + 2)/(1(2x + 5))) + 3) + 5) - 5 and g(x) = (1(-3(-5((2x - 3)/(2x - 3)) - 4)^2 - 1(-5((2x - 3)/(2x - 3)) - 4) - 1) + 3)/(-3(-3(-5((2x - 3)/(2x - 3)) - 4)^2 - 1(-5((2x - 3)/(2x - 3)) - 4) - 1) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 4((-1(1e^(-1((-3((2x - 3)/(-1x + 3)) + 2)/(1((2x - 3)/(-1x + 3)) - 3))) - 3) - 1)/(-3(1e^(-1((-3((2x - 3)/(-1x + 3)) + 2)/(1((2x - 3)/(-1x + 3)) - 3))) - 3) + 2))^2 + 3((-1(1e^(-1((-3((2x - 3)/(-1x + 3)) + 2)/(1((2x - 3)/(-1x + 3)) - 3))) - 3) - 1)/(-3(1e^(-1((-3((2x - 3)/(-1x + 3)) + 2)/(1((2x - 3)/(-1x + 3)) - 3))) - 3) + 2)) - 5 and g(x) = (-2(-4((1(-1x^2 - 4x + 4) + 2)/(-1(-1x^2 - 4x + 4) + 3))^2 - 3((1(-1x^2 - 4x + 4) + 2)/(-1(-1x^2 - 4x + 4) + 3)) - 1))/(-3(-4((1(-1x^2 - 4x + 4) + 2)/(-1(-1x^2 - 4x + 4) + 3))^2 - 3((1(-1x^2 - 4x + 4) + 2)/(-1(-1x^2 - 4x + 4) + 3)) - 1)) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1(-5((-1((2(-3x - 3) - 2)/(-2(-3x - 3) - 3)) - 1)/(3((2(-3x - 3) - 2)/(-2(-3x - 3) - 3)) + 2)) - 3) - 5 and g(x) = (1(2|((2(2e^(-1x) - 3) + 1)/(1(2e^(-1x) - 3))) + 1| + 3) + 1)/(-2(2|((2(2e^(-1x) - 3) + 1)/(1(2e^(-1x) - 3))) + 1| + 3) + 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1(1(-5(-5((3x + 1)/(1x)) - 4) + 1)) + 1)/(-1(1(-5(-5((3x + 1)/(1x)) - 4) + 1)) + 2) and g(x) = (-1((-2(-3(1x^2 + 3) + 4) + 1)/(3(-3(1x^2 + 3) + 4) - 1)) + 2)/(2((-2(-3(1x^2 + 3) + 4) + 1)/(3(-3(1x^2 + 3) + 4) - 1)) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -4(-3(1|((-3((3x + 3)/(3x + 3)) - 3)/(-1((3x + 3)/(3x + 3)) - 1)) + 2| + 3)^2 - 4(1|((-3((3x + 3)/(3x + 3)) - 3)/(-1((3x + 3)/(3x + 3)) - 1)) + 2| + 3) + 3) + 4 and g(x) = 1(2(-5((3x + 1)/(-3x)) + 1)^2 + 2(-5((3x + 1)/(-3x)) + 1) + 5) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-1(-1((-3(3|((-2x - 2)/(-3x - 3)) - 1|) - 3)/(-1(3|((-2x - 2)/(-3x - 3)) - 1|) - 2))^2 + 5((-3(3|((-2x - 2)/(-3x - 3)) - 1|) - 3)/(-1(3|((-2x - 2)/(-3x - 3)) - 1|) - 2)) - 5) - 2)/(-2(-1((-3(3|((-2x - 2)/(-3x - 3)) - 1|) - 3)/(-1(3|((-2x - 2)/(-3x - 3)) - 1|) - 2))^2 + 5((-3(3|((-2x - 2)/(-3x - 3)) - 1|) - 3)/(-1(3|((-2x - 2)/(-3x - 3)) - 1|) - 2)) - 5) + 3) and g(x) = -5((2(3(-1|x - 2| + 1) + 3) + 2)/(3(3(-1|x - 2| + 1) + 3) + 1)) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-3(-3(1|(5(-1|x + 1| - 3) + 1) - 2| - 2) - 1) + 3)/(-1(-3(1|(5(-1|x + 1| - 3) + 1) - 2| - 2) - 1) + 3) and g(x) = (-2(5((-1(2|x - 1| - 2) - 2)/(1(2|x - 1| - 2) - 3)) - 5) + 1)/(2(5((-1(2|x - 1| - 2) - 2)/(1(2|x - 1| - 2) - 3)) - 5) + 3) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3|(4(2|((-1(1x^2 - 4x - 1) - 3)/(-2(1x^2 - 4x - 1) + 3)) - 3| + 2)^2 + 3(2|((-1(1x^2 - 4x - 1) - 3)/(-2(1x^2 - 4x - 1) + 3)) - 3| + 2) + 2) + 3| + 3 and g(x) = -4(1(1e^(-1(-4x^2 - 3))) - 4) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (2(1(-1(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2)^2 + 4(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2) + 2)^2 + 4(-1(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2)^2 + 4(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2) + 2) + 5) + 2)/(-2(1(-1(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2)^2 + 4(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2) + 2)^2 + 4(-1(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2)^2 + 4(-2cos(2\u03c0(2|x + 3| + 2) - 3) + 2) + 2) + 5) - 1) and g(x) = 4((2(-1|(-3|x + 3| - 2) + 3| + 3) + 3)/(-1(-1|(-3|x + 3| - 2) + 3| + 3) + 2)) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(3((-1(3|(-2x^2 + 2x + 1) + 2| + 3) - 1)/(1(3|(-2x^2 + 2x + 1) + 2| + 3) + 3))^2 + 3) - 1 and g(x) = 1|((2(5(5x)^2 + 2(5x) + 2) - 3)/(-1(5(5x)^2 + 2(5x) + 2) - 3))| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3((2(5(-2(1x^2 + 4x))^2 + 5(-2(1x^2 + 4x)) + 4) - 1)/(-2(5(-2(1x^2 + 4x))^2 + 5(-2(1x^2 + 4x)) + 4) - 2))^2 + 2((2(5(-2(1x^2 + 4x))^2 + 5(-2(1x^2 + 4x)) + 4) - 1)/(-2(5(-2(1x^2 + 4x))^2 + 5(-2(1x^2 + 4x)) + 4) - 2)) + 5 and g(x) = -1(-4(-4(4x - 5) + 3)^2 + 2(-4(4x - 5) + 3) + 5) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2sin(1\u03c0(3|(1|(-5(-2|x + 2|)^2 + 4(-2|x + 2|) + 3) - 2| - 3) + 3| - 1) - 1) + 2 and g(x) = (1(-5(5(4x^2 + 5x + 2)^2 - 1(4x^2 + 5x + 2) - 5)))/(-1(-5(5(4x^2 + 5x + 2)^2 - 1(4x^2 + 5x + 2) - 5)) + 3) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1((3((-1(5(-2x^2 + 3x) + 5) - 2)/(1(5(-2x^2 + 3x) + 5) + 1)) + 1)/(2((-1(5(-2x^2 + 3x) + 5) - 2)/(1(5(-2x^2 + 3x) + 5) + 1)) + 2)) + 4 and g(x) = (3(3|(3(3sin(1\u03c0x - 3) + 1)^2 - 4(3sin(1\u03c0x - 3) + 1) + 5) - 2| + 2) + 2)/(2(3|(3(3sin(1\u03c0x - 3) + 1)^2 - 4(3sin(1\u03c0x - 3) + 1) + 5) - 2| + 2) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -1((-3(3|(1(5x - 2) - 3) - 1| - 2) + 3)/(2(3|(1(5x - 2) - 3) - 1| - 2) - 1)) + 5 and g(x) = 4(1|((3(1sin(2\u03c0x + 1) + 2) + 1)/(-1(1sin(2\u03c0x + 1) + 2) - 3)) + 2| + 3)^2 - 4(1|((3(1sin(2\u03c0x + 1) + 2) + 1)/(-1(1sin(2\u03c0x + 1) + 2) - 3)) + 2| + 3) + 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-1((1((3(-1|((-2x - 2)/(-3x - 2))| + 1) + 1)/(1(-1|((-2x - 2)/(-3x - 2))| + 1))) - 3)/(-3((3(-1|((-2x - 2)/(-3x - 2))| + 1) + 1)/(1(-1|((-2x - 2)/(-3x - 2))| + 1))) - 2)) + 3)/(-3((1((3(-1|((-2x - 2)/(-3x - 2))| + 1) + 1)/(1(-1|((-2x - 2)/(-3x - 2))| + 1))) - 3)/(-3((3(-1|((-2x - 2)/(-3x - 2))| + 1) + 1)/(1(-1|((-2x - 2)/(-3x - 2))| + 1))) - 2)) + 1) and g(x) = (1(1(-5(2cos(3\u03c0x - 1) - 2) + 2) + 4) + 2)/(3(1(-5(2cos(3\u03c0x - 1) - 2) + 2) + 4) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1((-2((-2(-1cos(3\u03c0((-2x)/(-1x - 2)) + 3) - 1) + 3)/(-2(-1cos(3\u03c0((-2x)/(-1x - 2)) + 3) - 1))) - 1)/(2((-2(-1cos(3\u03c0((-2x)/(-1x - 2)) + 3) - 1) + 3)/(-2(-1cos(3\u03c0((-2x)/(-1x - 2)) + 3) - 1))))) - 3 and g(x) = -2|((3(-2cos(2\u03c0(2x^2 - 1x + 5) + 3) - 1) - 1)/(-2(-2cos(2\u03c0(2x^2 - 1x + 5) + 3) - 1) + 3)) + 1| + 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1(-2cos(3\u03c0((-3(4(2x^2 + 3x + 5)^2 - 1(2x^2 + 3x + 5)) - 3)/(3(4(2x^2 + 3x + 5)^2 - 1(2x^2 + 3x + 5)) + 1)) + 3) - 2) + 1 and g(x) = 1|(-2|((-3((1x - 2)/(-2x)) - 3)/(-3((1x - 2)/(-2x)) + 2)) - 2| + 3) - 3| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 1|(-1((3((-3(-4x^2 - 4x + 2) + 3)/(3(-4x^2 - 4x + 2) - 2)) - 1)/(-1((-3(-4x^2 - 4x + 2) + 3)/(3(-4x^2 - 4x + 2) - 2)) + 3)) + 4) + 1| - 3 and g(x) = 5(3|(2e^(-1((2x - 3)/(3x + 1))) - 1) - 3| - 1)^2 + 3(3|(2e^(-1((2x - 3)/(3x + 1))) - 1) - 3| - 1) - 5 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2(-4(-1(2(-4x^2 + 3) + 1) + 4) + 1) + 4 and g(x) = (3((-3(-4(2x^2 + 4x - 3)^2 - 4) + 2)/(1(-4(2x^2 + 4x - 3)^2 - 4) + 1)) - 3)/(-3((-3(-4(2x^2 + 4x - 3)^2 - 4) + 2)/(1(-4(2x^2 + 4x - 3)^2 - 4) + 1)) - 3) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-1(-1|((-2(3e^(2(1x^2 - 3x - 1)) + 2) - 3)/(-1(3e^(2(1x^2 - 3x - 1)) + 2) - 3))| + 1) - 1)/(-2(-1|((-2(3e^(2(1x^2 - 3x - 1)) + 2) - 3)/(-1(3e^(2(1x^2 - 3x - 1)) + 2) - 3))| + 1) + 1) and g(x) = (2((-1(5(-3|x + 2| - 1)^2 + 4(-3|x + 2| - 1) - 2) + 2)/(2(5(-3|x + 2| - 1)^2 + 4(-3|x + 2| - 1) - 2) + 1)) + 1)/(-3((-1(5(-3|x + 2| - 1)^2 + 4(-3|x + 2| - 1) - 2) + 2)/(2(5(-3|x + 2| - 1)^2 + 4(-3|x + 2| - 1) - 2) + 1)) - 3) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1(1((-2(-4(4x + 4)^2 + 5(4x + 4) + 5) + 2)/(1(-4(4x + 4)^2 + 5(4x + 4) + 5))) + 3) - 1 and g(x) = -1|(5(-3cos(1\u03c0(-2|x + 3| + 3) - 1)) + 3) + 1| - 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -4(2(5(1|(-5x - 5) - 3| - 1) + 2)^2 + 2(5(1|(-5x - 5) - 3| - 1) + 2) - 1) + 5 and g(x) = -2|(-2(-3|(-4x^2 + 3x - 2)| - 2)^2 - 3(-3|(-4x^2 + 3x - 2)| - 2)) - 3| + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1|(2|(-3e^(-2((-3((-3x + 2)/(3x + 3)) + 1)/(-2((-3x + 2)/(3x + 3)) + 3))) - 2) + 1| - 3) - 2| - 2 and g(x) = (-3(-4(3|((-1x + 2)/(2x - 1)) + 3| - 2) + 5))/(2(-4(3|((-1x + 2)/(2x - 1)) + 3| - 2) + 5) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -4((2(1((1(2e^(2x)) + 1)/(1(2e^(2x)))) + 4) - 1)/(2(1((1(2e^(2x)) + 1)/(1(2e^(2x)))) + 4) - 3))^2 - 1((2(1((1(2e^(2x)) + 1)/(1(2e^(2x)))) + 4) - 1)/(2(1((1(2e^(2x)) + 1)/(1(2e^(2x)))) + 4) - 3)) + 4 and g(x) = -3|((1(-1cos(1\u03c0(5x^2 + 4x - 5) + 2) + 2) + 3)/(-1(-1cos(1\u03c0(5x^2 + 4x - 5) + 2) + 2) - 3)) - 1| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|(-5(3|(5(2cos(1\u03c0x - 2) + 2)^2 + 4(2cos(1\u03c0x - 2) + 2) + 1) - 2| - 3) + 3) - 3| + 2 and g(x) = 4(-3e^(-1(1|(-1x^2 + 3x + 1)|)) + 2) + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (2(-1((2(1(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 1) - 2)/(3(1(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 1) - 2))^2 + 5((2(1(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 1) - 2)/(3(1(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 1) - 2)) + 3) - 2)/(2(-1((2(1(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 1) - 2)/(3(1(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 1) - 2))^2 + 5((2(1(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 1) - 2)/(3(1(-1|x + 1| + 2)^2 - 4(-1|x + 1| + 2) - 1) - 2)) + 3) - 1) and g(x) = (3((-1((3(-5x^2 - 5x + 3) - 1)/(1(-5x^2 - 5x + 3) - 3)) - 3)/(3((3(-5x^2 - 5x + 3) - 1)/(1(-5x^2 - 5x + 3) - 3)) - 2)) - 2)/(-1((-1((3(-5x^2 - 5x + 3) - 1)/(1(-5x^2 - 5x + 3) - 3)) - 3)/(3((3(-5x^2 - 5x + 3) - 1)/(1(-5x^2 - 5x + 3) - 3)) - 2)) - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-3(-1|(2cos(1\u03c0(-2|(-2x^2 - 2x - 4) + 1| + 3) - 1) - 3) - 2|) + 3)/(1(-1|(2cos(1\u03c0(-2|(-2x^2 - 2x - 4) + 1| + 3) - 1) - 3) - 2|) + 1) and g(x) = (1(-1((1(2x + 2) + 3)/(2(2x + 2) + 3))^2 - 3((1(2x + 2) + 3)/(2(2x + 2) + 3)) + 5) - 2)/(-3(-1((1(2x + 2) + 3)/(2(2x + 2) + 3))^2 - 3((1(2x + 2) + 3)/(2(2x + 2) + 3)) + 5) - 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 5(2((-3(-2e^(-2(2x^2 + 3x - 1)) + 2) - 2)/(1(-2e^(-2(2x^2 + 3x - 1)) + 2) + 1)) + 3) - 5 and g(x) = 1|(3((2(4x - 1) + 1)/(-3(4x - 1) + 2)) + 1) - 2| + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3(1((1(3(1x - 2)^2 - 4(1x - 2)) + 3)/(-3(3(1x - 2)^2 - 4(1x - 2)) - 3))^2 - 2((1(3(1x - 2)^2 - 4(1x - 2)) + 3)/(-3(3(1x - 2)^2 - 4(1x - 2)) - 3)) + 5) and g(x) = 3(-1((-1((2x + 1)/(2x + 3)) + 1)/(2((2x + 1)/(2x + 3)) - 3)) + 3) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -5(-1(-3(-3((1x - 2)/(1x + 2)))) - 2) + 4 and g(x) = (3(1(-1cos(3\u03c0(-3|x + 1| - 3) - 1) + 3)^2 + 1(-1cos(3\u03c0(-3|x + 1| - 3) - 1) + 3) - 5))/(1(1(-1cos(3\u03c0(-3|x + 1| - 3) - 1) + 3)^2 + 1(-1cos(3\u03c0(-3|x + 1| - 3) - 1) + 3) - 5) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -3(5(1(1(3sin(1\u03c0x + 3) + 3)^2 - 4(3sin(1\u03c0x + 3) + 3) + 5)^2 + 4(1(3sin(1\u03c0x + 3) + 3)^2 - 4(3sin(1\u03c0x + 3) + 3) + 5) - 2) + 1) - 1 and g(x) = (2(-2e^(1(1|(-2|x + 2| - 2) + 3| - 2)) + 2) - 1)/(-3(-2e^(1(1|(-2|x + 2| - 2) + 3| - 2)) + 2) - 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -4(-5((-1(4(-2|x - 3| - 1)^2 + 1(-2|x - 3| - 1) - 2) + 1)/(3(4(-2|x - 3| - 1)^2 + 1(-2|x - 3| - 1) - 2) + 3)) - 5) + 4 and g(x) = 1|(-1(-1|(-2x - 1) + 3| - 3) - 4) + 1| - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (3(-1(1(-1((-2x + 3)/(-1x - 1)) - 5)^2 + 2(-1((-2x + 3)/(-1x - 1)) - 5) - 3) + 2))/(-2(-1(1(-1((-2x + 3)/(-1x - 1)) - 5)^2 + 2(-1((-2x + 3)/(-1x - 1)) - 5) - 3) + 2) - 3) and g(x) = 2(-2e^(1(4(-3x - 5) - 4)) - 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3(1|(2|(-4(1x + 4)^2 - 1) - 1| + 2)| + 1) - 4 and g(x) = 3((-3(2((-1x - 1)/(3x - 2)) + 2) - 1)/(-3(2((-1x - 1)/(3x - 2)) + 2) + 4))^2 + 2((-3(2((-1x - 1)/(3x - 2)) + 2) - 1)/(-3(2((-1x - 1)/(3x - 2)) + 2) + 4)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -5((2((2(-2((-3x - 3)/(3x - 2))^2 + 1) - 2)/(-1(-2((-3x - 3)/(3x - 2))^2 + 1))))/(-2((2(-2((-3x - 3)/(3x - 2))^2 + 1) - 2)/(-1(-2((-3x - 3)/(3x - 2))^2 + 1))) - 3))^2 + 5((2((2(-2((-3x - 3)/(3x - 2))^2 + 1) - 2)/(-1(-2((-3x - 3)/(3x - 2))^2 + 1))))/(-2((2(-2((-3x - 3)/(3x - 2))^2 + 1) - 2)/(-1(-2((-3x - 3)/(3x - 2))^2 + 1))) - 3)) + 4 and g(x) = -1sin(2\u03c0(3|((-1((3x + 3)/(1x + 2)) - 1)/(-3((3x + 3)/(1x + 2)) - 3)) + 3| + 3) - 1) - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -2(3(1sin(2\u03c0(-1|(5x^2 + 2x + 2)|)) + 3)) - 3 and g(x) = (1((1(4((-2x)/(2x + 1)) + 3) + 2)/(-3(4((-2x)/(2x + 1)) + 3))))/(3((1(4((-2x)/(2x + 1)) + 3) + 2)/(-3(4((-2x)/(2x + 1)) + 3))) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -4((2(-4(1e^(1(3x^2 + 1x + 5)) - 1)^2 + 5(1e^(1(3x^2 + 1x + 5)) - 1) - 1) + 3)/(-3(-4(1e^(1(3x^2 + 1x + 5)) - 1)^2 + 5(1e^(1(3x^2 + 1x + 5)) - 1) - 1) + 4))^2 + 2((2(-4(1e^(1(3x^2 + 1x + 5)) - 1)^2 + 5(1e^(1(3x^2 + 1x + 5)) - 1) - 1) + 3)/(-3(-4(1e^(1(3x^2 + 1x + 5)) - 1)^2 + 5(1e^(1(3x^2 + 1x + 5)) - 1) - 1) + 4)) - 5 and g(x) = (2((-2(1(2x^2 - 5x - 4) - 3))/(-1(1(2x^2 - 5x - 4) - 3) - 3)) - 2)/(-1((-2(1(2x^2 - 5x - 4) - 3))/(-1(1(2x^2 - 5x - 4) - 3) - 3))) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -4(-2|(-2|((-2((-2x - 1)/(2x + 2)) - 2)/(1((-2x - 1)/(2x + 2)) - 2)) - 1| - 3) + 2| + 2) + 3 and g(x) = 2|(-5(4(1cos(3\u03c0x - 2) - 1)^2 + 3(1cos(3\u03c0x - 2) - 1) + 5)^2 + 3(4(1cos(3\u03c0x - 2) - 1)^2 + 3(1cos(3\u03c0x - 2) - 1) + 5) - 1) + 2| - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1((3((-2(2(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 5) - 1)/(-1(2(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 5))) + 1)/(1((-2(2(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 5) - 1)/(-1(2(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 5)))))^2 + 4((3((-2(2(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 5) - 1)/(-1(2(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 5))) + 1)/(1((-2(2(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 5) - 1)/(-1(2(-3|x - 2| - 2)^2 - 5(-3|x - 2| - 2) + 5))))) - 5 and g(x) = 1((3(-2(2x + 3) - 5))/(-2(-2(2x + 3) - 5) + 3)) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (2(-1((2((3(-3x + 2) + 3)/(-3(-3x + 2) + 2)) + 2)/(-1((3(-3x + 2) + 3)/(-3(-3x + 2) + 2)) - 2)) - 4))/(1(-1((2((3(-3x + 2) + 3)/(-3(-3x + 2) + 2)) + 2)/(-1((3(-3x + 2) + 3)/(-3(-3x + 2) + 2)) - 2)) - 4) + 3) and g(x) = (2(2(1(1x + 3) + 1)^2 + 1(1(1x + 3) + 1) + 5) + 2)/(2(2(1(1x + 3) + 1)^2 + 1(1(1x + 3) + 1) + 5) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1|(1(-4(1e^(1((-1x - 3)/(-2x))) - 2)) + 5) + 3| + 2 and g(x) = 3((1((-3(3e^(1x) - 1) + 2)/(-2(3e^(1x) - 1) - 3)) + 3)/(-2((-3(3e^(1x) - 1) + 2)/(-2(3e^(1x) - 1) - 3)) + 3))^2 - 3((1((-3(3e^(1x) - 1) + 2)/(-2(3e^(1x) - 1) - 3)) + 3)/(-2((-3(3e^(1x) - 1) + 2)/(-2(3e^(1x) - 1) - 3)) + 3)) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1|((2(4((3(-3|x - 2|) + 3)/(-2(-3|x - 2|) - 1)) + 3) - 1)/(3(4((3(-3|x - 2|) + 3)/(-2(-3|x - 2|) - 1)) + 3) + 1)) + 1| - 2 and g(x) = -3(1(1(1|x + 1| - 3)^2 - 3(1|x + 1| - 3) + 5) + 2)^2 - 1(1(1(1|x + 1| - 3)^2 - 3(1|x + 1| - 3) + 5) + 2) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (3(-2|(1((3(-2x - 3) - 3)/(-1(-2x - 3) + 3)) + 1) + 3| + 2) + 1)/(-3(-2|(1((3(-2x - 3) - 3)/(-1(-2x - 3) + 3)) + 1) + 3| + 2) + 1) and g(x) = -3(4((3(-5x - 1) - 1)/(2(-5x - 1) + 1)) + 4) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1(-1|((3((3((2x - 2)/(-1x - 1)) - 1)/(2((2x - 2)/(-1x - 1)) + 1)) - 2)/(-1((3((2x - 2)/(-1x - 1)) - 1)/(2((2x - 2)/(-1x - 1)) + 1)) + 2)) + 3| + 1) - 1)/(-1(-1|((3((3((2x - 2)/(-1x - 1)) - 1)/(2((2x - 2)/(-1x - 1)) + 1)) - 2)/(-1((3((2x - 2)/(-1x - 1)) - 1)/(2((2x - 2)/(-1x - 1)) + 1)) + 2)) + 3| + 1) - 3) and g(x) = (-3(5(-4(2x^2 - 3x + 3)) + 2))/(-1(5(-4(2x^2 - 3x + 3)) + 2) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (2(1|(-1(3|(1e^(-1x) - 3)| - 3) - 2) - 3| + 1))/(-2(1|(-1(3|(1e^(-1x) - 3)| - 3) - 2) - 3| + 1)) and g(x) = (-1((1(-1e^(2(-4x - 3)) + 1) + 1)/(2(-1e^(2(-4x - 3)) + 1) - 1)) + 3)/(-2((1(-1e^(2(-4x - 3)) + 1) + 1)/(2(-1e^(2(-4x - 3)) + 1) - 1)) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1(1(2|(4(5x - 3)) - 1| + 1)^2 - 4(2|(4(5x - 3)) - 1| + 1) + 4))/(2(1(2|(4(5x - 3)) - 1| + 1)^2 - 4(2|(4(5x - 3)) - 1| + 1) + 4) + 3) and g(x) = -2|((-3((2((-3x + 1)/(3x - 2)) + 2)/(2((-3x + 1)/(3x - 2)) + 2)) - 2)/(-1((2((-3x + 1)/(3x - 2)) + 2)/(2((-3x + 1)/(3x - 2)) + 2)) - 2))| + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3|((1(-3((-1(-1|x - 1| - 2))/(1(-1|x - 1| - 2) - 3)) + 1) + 1)/(1(-3((-1(-1|x - 1| - 2))/(1(-1|x - 1| - 2) - 3)) + 1) + 2)) + 3| and g(x) = 3(2(-2((-3x + 1)/(-2x + 3)) - 5) + 5) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1(1(5(-2|((3x + 3)/(3x + 2)) - 3| + 1)^2 - 5(-2|((3x + 3)/(3x + 2)) - 3| + 1) + 2)^2 + 1(5(-2|((3x + 3)/(3x + 2)) - 3| + 1)^2 - 5(-2|((3x + 3)/(3x + 2)) - 3| + 1) + 2) + 1) + 2)/(-2(1(5(-2|((3x + 3)/(3x + 2)) - 3| + 1)^2 - 5(-2|((3x + 3)/(3x + 2)) - 3| + 1) + 2)^2 + 1(5(-2|((3x + 3)/(3x + 2)) - 3| + 1)^2 - 5(-2|((3x + 3)/(3x + 2)) - 3| + 1) + 2) + 1) + 3) and g(x) = (-1((1((3(-2x - 4) + 3)/(-1(-2x - 4))) + 1)/(-2((3(-2x - 4) + 3)/(-1(-2x - 4))))) + 3)/(1((1((3(-2x - 4) + 3)/(-1(-2x - 4))) + 1)/(-2((3(-2x - 4) + 3)/(-1(-2x - 4))))) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1|(1(2|(2|(1|x - 3| + 2)| - 1) - 3|) - 2) + 1| + 1 and g(x) = -1e^(2(-1(-3(-2|x - 3| - 3)^2 + 5(-2|x - 3| - 3) - 1)^2 - 1(-3(-2|x - 3| - 3)^2 + 5(-2|x - 3| - 3) - 1) + 2)) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -1cos(2\u03c0((1(2|(-2|(3|x - 1| - 1)|) + 1| - 3) - 2)/(3(2|(-2|(3|x - 1| - 1)|) + 1| - 3))) + 2) and g(x) = (2((-2(1(2|x| - 3) - 1))/(-3(1(2|x| - 3) - 1) + 2)) - 3)/(-3((-2(1(2|x| - 3) - 1))/(-3(1(2|x| - 3) - 1) + 2))) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -2(2|(-3|(1|((1x + 1)/(-1x + 2))|) - 2| + 2) + 1|)^2 - 2(2|(-3|(1|((1x + 1)/(-1x + 2))|) - 2| + 2) + 1|) - 2 and g(x) = -1|(-1((1(-2|x + 2| - 2) + 2)/(2(-2|x + 2| - 2) + 1))^2 + 5((1(-2|x + 2| - 2) + 2)/(2(-2|x + 2| - 2) + 1)) - 5)| + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 5(-3(5((1(-1x^2 + 3x - 4) - 2)/(-2(-1x^2 + 3x - 4) + 1)) - 3)^2 + 2(5((1(-1x^2 + 3x - 4) - 2)/(-2(-1x^2 + 3x - 4) + 1)) - 3) - 1) - 1 and g(x) = -3(2|(2(-1x - 1) - 3) - 2| + 1)^2 - 1(2|(2(-1x - 1) - 3) - 2| + 1) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 1((1(-4(-3(2x^2 - 2x + 2)^2 - 3(2x^2 - 2x + 2) + 4) + 2) + 1)/(-3(-4(-3(2x^2 - 2x + 2)^2 - 3(2x^2 - 2x + 2) + 4) + 2) - 2)) - 4 and g(x) = -1(4((2(-5x + 5) - 2)/(1(-5x + 5) - 3))^2 + 1) + 5 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1(-3(-5(-2(3|x + 2| + 1)^2 + 1) - 3)^2 + 4(-5(-2(3|x + 2| + 1)^2 + 1) - 3) - 2)^2 - 4(-3(-5(-2(3|x + 2| + 1)^2 + 1) - 3)^2 + 4(-5(-2(3|x + 2| + 1)^2 + 1) - 3) - 2) + 5 and g(x) = -1(-3|((1(-2x + 1) - 2)/(1(-2x + 1) + 2)) + 1| + 1)^2 + 1(-3|((1(-2x + 1) - 2)/(1(-2x + 1) + 2)) + 1| + 1) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 1(-2(3(1((-3x + 1)/(3x + 2)) + 3) + 5)^2 - 1(3(1((-3x + 1)/(3x + 2)) + 3) + 5) + 3) - 1 and g(x) = -3|(-2|(1(-1sin(1\u03c0x - 3) + 2))|) + 3| + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 3(1|(1(-1e^(2(-1x^2 - 4x + 1)) + 2) + 1) - 2| + 1)^2 - 3(1|(1(-1e^(2(-1x^2 - 4x + 1)) + 2) + 1) - 2| + 1) - 2 and g(x) = 1(3(-5(2x^2 + 3x + 1) - 3)^2 - 1(-5(2x^2 + 3x + 1) - 3) + 4) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 5(1|(1(1(2x + 1) + 5) + 4) + 3| - 1) + 5 and g(x) = (3(-4(3(5x^2 - 2x + 2)^2 + 3)^2 - 1(3(5x^2 - 2x + 2)^2 + 3) + 5) + 2)/(2(-4(3(5x^2 - 2x + 2)^2 + 3)^2 - 1(3(5x^2 - 2x + 2)^2 + 3) + 5) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-13", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1sin(3\u03c0(5(-4((1(2x - 5) + 1)/(-1(2x - 5) - 1))^2 - 2((1(2x - 5) + 1)/(-1(2x - 5) - 1)))^2 - 5(-4((1(2x - 5) + 1)/(-1(2x - 5) - 1))^2 - 2((1(2x - 5) + 1)/(-1(2x - 5) - 1)))) - 3) and g(x) = -2|(2|(1(5x^2 + 3x + 5) - 3) - 1| - 1)| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1(3|(-5(2(1cos(3\u03c0x - 3) + 3) - 3) + 2) - 1| + 3)^2 + 5 and g(x) = -4(5((-2(-5x - 3) - 2)/(2(-5x - 3)))^2 - 5((-2(-5x - 3) - 2)/(2(-5x - 3))) - 3) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2(4(-1(-1(-1|x - 3| + 2) - 1)^2 - 4)^2 - 5(-1(-1(-1|x - 3| + 2) - 1)^2 - 4) + 1) + 2 and g(x) = 3|(-1(-5(3x - 2)^2 + 1(3x - 2) - 2)^2 - 1(-5(3x - 2)^2 + 1(3x - 2) - 2) - 2) - 2| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-2(1(2(4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 2)^2 - 2(4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 2) + 2)^2 - 3(2(4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 2)^2 - 2(4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 2) + 2) + 3) - 3)/(1(1(2(4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 2)^2 - 2(4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 2) + 2)^2 - 3(2(4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 2)^2 - 2(4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 2) + 2) + 3) + 2) and g(x) = (3(-3(-2(1x - 2) - 1) + 3) - 3)/(1(-3(-2(1x - 2) - 1) + 3) - 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 4(-2|(4(-1cos(2\u03c0((-2x + 1)/(-2x - 1)) - 2) + 3) - 2) + 1| + 2) and g(x) = -1((3(-2|(3x - 3) - 2| - 2) - 3)/(1(-2|(3x - 3) - 2| - 2) + 3)) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-1(-1(-2((-1(1x^2 - 4x - 3) + 1)/(1(1x^2 - 4x - 3) + 2)) - 2)^2 - 1(-2((-1(1x^2 - 4x - 3) + 1)/(1(1x^2 - 4x - 3) + 2)) - 2) - 4))/(2(-1(-2((-1(1x^2 - 4x - 3) + 1)/(1(1x^2 - 4x - 3) + 2)) - 2)^2 - 1(-2((-1(1x^2 - 4x - 3) + 1)/(1(1x^2 - 4x - 3) + 2)) - 2) - 4) + 1) and g(x) = 5((-2(3e^(-1(3|x - 1| - 3))) + 3)/(-1(3e^(-1(3|x - 1| - 3))) + 2)) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 4(1((-1((3(-2x + 3) + 1)/(-2(-2x + 3) + 3)))/(-3((3(-2x + 3) + 1)/(-2(-2x + 3) + 3)) + 4)) - 3) + 3 and g(x) = -1(4(-5(-1|x - 1|) - 5) + 1) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3|(3(4(-4(1|x - 2| - 3) - 2) - 3)^2 - 3(4(-4(1|x - 2| - 3) - 2) - 3) - 2)| + 1 and g(x) = -5((-3(1(3x - 3)^2 + 3(3x - 3) - 2) - 2)/(1(1(3x - 3)^2 + 3(3x - 3) - 2) - 3)) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -2|(3(3cos(2\u03c0((1(-5x^2 + 1x - 3) + 2)/(-3(-5x^2 + 1x - 3) + 2))) - 3) + 3) + 2| + 1 and g(x) = (1((-2((-2(1x^2 - 4x - 1) - 1)/(3(1x^2 - 4x - 1) - 1)) + 3)/(2((-2(1x^2 - 4x - 1) - 1)/(3(1x^2 - 4x - 1) - 1)) - 1)) - 3)/(2((-2((-2(1x^2 - 4x - 1) - 1)/(3(1x^2 - 4x - 1) - 1)) + 3)/(2((-2(1x^2 - 4x - 1) - 1)/(3(1x^2 - 4x - 1) - 1)) - 1)) + 3) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (3((3(1((-1(-1x^2 - 3x + 3))/(3(-1x^2 - 3x + 3) + 1)) - 2) + 2)/(2(1((-1(-1x^2 - 3x + 3))/(3(-1x^2 - 3x + 3) + 1)) - 2) + 3)) + 1)/(-1((3(1((-1(-1x^2 - 3x + 3))/(3(-1x^2 - 3x + 3) + 1)) - 2) + 2)/(2(1((-1(-1x^2 - 3x + 3))/(3(-1x^2 - 3x + 3) + 1)) - 2) + 3)) - 3) and g(x) = -1(-2|(-2sin(2\u03c0((3x - 2)/(3x - 2)) + 1) - 1) + 2|) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1|((-1(2|(-3(-2|x + 3| - 3)^2 + 1(-2|x + 3| - 3)) + 1|))/(-1(2|(-3(-2|x + 3| - 3)^2 + 1(-2|x + 3| - 3)) + 1|) + 2)) - 1| - 2 and g(x) = 3(-1|(-2|(-1x - 4) - 1| - 2) + 3| - 2) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (2(-1(4(1(-1x + 4)^2 - 1(-1x + 4) + 2) - 2) + 4) + 3)/(3(-1(4(1(-1x + 4)^2 - 1(-1x + 4) + 2) - 2) + 4) - 1) and g(x) = (1(-2|(1((-1x - 2)/(2x + 3))^2 - 3((-1x - 2)/(2x + 3)) + 1) - 1| + 1) + 3)/(2(-2|(1((-1x - 2)/(2x + 3))^2 - 3((-1x - 2)/(2x + 3)) + 1) - 1| + 1) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(1sin(3\u03c0((-2(-1|(-2|x - 2| - 1) - 3|) + 2)/(1(-1|(-2|x - 2| - 1) - 3|) - 3)))) - 3| and g(x) = 5(-3(-2((-2x + 1)/(3x + 1))^2 - 2((-2x + 1)/(3x + 1)) + 4) - 2) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3((2((1(2e^(1(-1|x| + 3)) - 3) - 3)/(-2(2e^(1(-1|x| + 3)) - 3) - 1)) + 2)/(-2((1(2e^(1(-1|x| + 3)) - 3) - 3)/(-2(2e^(1(-1|x| + 3)) - 3) - 1)) + 3)) - 3)/(3((2((1(2e^(1(-1|x| + 3)) - 3) - 3)/(-2(2e^(1(-1|x| + 3)) - 3) - 1)) + 2)/(-2((1(2e^(1(-1|x| + 3)) - 3) - 3)/(-2(2e^(1(-1|x| + 3)) - 3) - 1)) + 3)) - 1) and g(x) = -4(2(-5((-2x)/(-2x - 1))^2 + 1((-2x)/(-2x - 1)) + 4)^2 - 1) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2|((1(3((1((-1x - 2)/(1x + 3)))/(1((-1x - 2)/(1x + 3)) + 1)) + 4) + 1)/(-1(3((1((-1x - 2)/(1x + 3)))/(1((-1x - 2)/(1x + 3)) + 1)) + 4) + 2)) - 3| + 1 and g(x) = 2|(3|(3|(-5x - 3)| + 1) + 3| + 1) + 1| + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2((2(-4(-2e^(-2((-3x + 2)/(2x - 3)))) - 2) + 2)/(1(-4(-2e^(-2((-3x + 2)/(2x - 3)))) - 2) + 3)) - 2 and g(x) = (-3(-2e^(1(-5(5x + 1) + 2)) - 2) - 1)/(-3(-2e^(1(-5(5x + 1) + 2)) - 2) - 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (3(-2|(1((-2((2x - 2)/(-3x + 2)) + 2)/(-2((2x - 2)/(-3x + 2)) - 2)) - 3)| - 1) - 2)/(2(-2|(1((-2((2x - 2)/(-3x + 2)) + 2)/(-2((2x - 2)/(-3x + 2)) - 2)) - 3)| - 1) + 1) and g(x) = -1((-3((3(-1sin(1\u03c0x - 1) - 1) - 2)/(-1(-1sin(1\u03c0x - 1) - 1) + 2)) - 2)/(1((3(-1sin(1\u03c0x - 1) - 1) - 2)/(-1(-1sin(1\u03c0x - 1) - 1) + 2)) - 3))^2 + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3(3(1((1(1e^(-1x) - 3) + 3)/(-1(1e^(-1x) - 3) + 2))) + 4)^2 + 3(3(1((1(1e^(-1x) - 3) + 3)/(-1(1e^(-1x) - 3) + 2))) + 4) - 1 and g(x) = 3|(3((1(3e^(-1x) + 2) - 3)/(2(3e^(-1x) + 2)))^2 - 1((1(3e^(-1x) + 2) - 3)/(2(3e^(-1x) + 2))) - 4) + 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1|(-5(1e^(1(1(-2|x + 1| + 3) + 1)) + 2)^2 + 5(1e^(1(1(-2|x + 1| + 3) + 1)) + 2) + 5) + 3| + 3 and g(x) = -1(-1((-3(-3|x|) - 2)/(-2(-3|x|) - 3)) + 1) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|(3|(-3((2(4x + 3) - 2)/(2(4x + 3) - 3))^2 - 5((2(4x + 3) - 2)/(2(4x + 3) - 3)) - 5) + 1|) - 2| - 1 and g(x) = 3(1(5(3x + 1) - 4)^2 - 5(5(3x + 1) - 4) - 4) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2(-1|(2|(-1(1x^2 + 1x - 2)^2 + 4(1x^2 + 1x - 2) - 4) - 3| - 3) - 2| - 1) + 2 and g(x) = 3e^(-1(-4((-1((-1x + 2)/(-1x - 2)) + 3)/(-2((-1x + 2)/(-1x - 2)) - 2))^2 + 4((-1((-1x + 2)/(-1x - 2)) + 3)/(-2((-1x + 2)/(-1x - 2)) - 2)) + 5)) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-1(3|(2e^(-2((-1(5x - 3) + 3)/(-1(5x - 3) + 2))) - 3) + 1| - 3) - 1)/(-2(3|(2e^(-2((-1(5x - 3) + 3)/(-1(5x - 3) + 2))) - 3) + 1| - 3) + 1) and g(x) = (-1(2((1(-1cos(3\u03c0x - 1) - 2) - 1)/(3(-1cos(3\u03c0x - 1) - 2) - 2)) - 3) + 2)/(1(2((1(-1cos(3\u03c0x - 1) - 2) - 1)/(3(-1cos(3\u03c0x - 1) - 2) - 2)) - 3) - 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 5(-5(2((-1(1x^2 + 1x - 3) - 1)/(-2(1x^2 + 1x - 3))) + 2) - 1) - 4 and g(x) = 1sin(2\u03c0(-2|(-1|(2|x - 3|) - 1| - 3) + 1| + 2) - 1) + 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (2(-4((2(-1(-3|x - 2| + 2)^2 + 2(-3|x - 2| + 2) + 3) + 1)/(3(-1(-3|x - 2| + 2)^2 + 2(-3|x - 2| + 2) + 3) + 2)) - 2) - 3)/(-2(-4((2(-1(-3|x - 2| + 2)^2 + 2(-3|x - 2| + 2) + 3) + 1)/(3(-1(-3|x - 2| + 2)^2 + 2(-3|x - 2| + 2) + 3) + 2)) - 2) + 3) and g(x) = 1|(3|((-1(5x - 3) + 2)/(1(5x - 3) + 2)) + 2|) + 1| - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(2|((3(-5((3x + 1)/(-2x - 1)) + 2) - 2)/(-3(-5((3x + 1)/(-2x - 1)) + 2) + 2)) - 1| - 3)^2 - 3(2|((3(-5((3x + 1)/(-2x - 1)) + 2) - 2)/(-3(-5((3x + 1)/(-2x - 1)) + 2) + 2)) - 1| - 3) + 4 and g(x) = 3(1((-2((2x)/(-1x - 3)) + 3)/(1((2x)/(-1x - 3)) + 2)) - 3)^2 + 1(1((-2((2x)/(-1x - 3)) + 3)/(1((2x)/(-1x - 3)) + 2)) - 3) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3((3(3|(4(3|x - 1| + 2) + 3) - 1| - 1) - 1)/(-2(3|(4(3|x - 1| + 2) + 3) - 1| - 1) + 3))^2 + 4((3(3|(4(3|x - 1| + 2) + 3) - 1| - 1) - 1)/(-2(3|(4(3|x - 1| + 2) + 3) - 1| - 1) + 3)) - 3 and g(x) = -3(1(3(1x)) - 3) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3((-1(1cos(3\u03c0(-2|(1x^2 - 5x) - 3| - 3) + 1)) + 1)/(-1(1cos(3\u03c0(-2|(1x^2 - 5x) - 3| - 3) + 1)) - 2)) + 3 and g(x) = (-2(-5(-1(2x^2 - 3x + 2) + 1) - 5) - 1)/(-3(-5(-1(2x^2 - 3x + 2) + 1) - 5) - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1|(-5(-1(-1|((3x + 3)/(-1x + 2)) + 2| + 3) + 5) - 3) + 3| - 3 and g(x) = -3|((1(5(-5x + 3) - 2) - 1)/(-2(5(-5x + 3) - 2) - 3)) - 3| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-2(1|(-2sin(2\u03c0(2|(5x - 1) + 1| - 3) - 2) + 1) - 3| + 3) - 1)/(-2(1|(-2sin(2\u03c0(2|(5x - 1) + 1| - 3) - 2) + 1) - 3| + 3) - 3) and g(x) = -1(-1(-4(-1x + 1)^2 + 5) - 3) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -2(5((-2(-5(1sin(3\u03c0x - 3) + 2)^2 + 2(1sin(3\u03c0x - 3) + 2) - 2))/(-2(-5(1sin(3\u03c0x - 3) + 2)^2 + 2(1sin(3\u03c0x - 3) + 2) - 2) + 1))^2 + 4((-2(-5(1sin(3\u03c0x - 3) + 2)^2 + 2(1sin(3\u03c0x - 3) + 2) - 2))/(-2(-5(1sin(3\u03c0x - 3) + 2)^2 + 2(1sin(3\u03c0x - 3) + 2) - 2) + 1)) - 5) + 2 and g(x) = -1|(2(-3(-4x - 5)^2 - 2) + 5) - 3| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1((2(1(-1((3x - 3)/(-1x - 2))^2 + 2((3x - 3)/(-1x - 2)) + 2) + 4))/(-1(1(-1((3x - 3)/(-1x - 2))^2 + 2((3x - 3)/(-1x - 2)) + 2) + 4) - 2))^2 + 4((2(1(-1((3x - 3)/(-1x - 2))^2 + 2((3x - 3)/(-1x - 2)) + 2) + 4))/(-1(1(-1((3x - 3)/(-1x - 2))^2 + 2((3x - 3)/(-1x - 2)) + 2) + 4) - 2)) + 1 and g(x) = (1(3|(2(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 2) + 2) + 2| - 2) - 3)/(-1(3|(2(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 2) + 2) + 2| - 2)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|(-1((1((-1(1x + 5) + 2)/(-3(1x + 5) - 3)) + 1)/(3((-1(1x + 5) + 2)/(-3(1x + 5) - 3)) - 1))^2 - 5((1((-1(1x + 5) + 2)/(-3(1x + 5) - 3)) + 1)/(3((-1(1x + 5) + 2)/(-3(1x + 5) - 3)) - 1)) + 2) - 3| - 1 and g(x) = 3((-2((1(1x - 1) - 1)/(2(1x - 1) - 3)) - 2)/(-3((1(1x - 1) - 1)/(2(1x - 1) - 3)) + 1)) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1(1(-2|(-3((-1x + 3)/(-3x - 2)) + 5) - 3| + 2)^2 - 5(-2|(-3((-1x + 3)/(-3x - 2)) + 5) - 3| + 2) + 1)^2 - 3 and g(x) = -1(-1e^(2(-3|(-1x^2 - 2x + 1) - 3| + 2)) + 1)^2 + 3(-1e^(2(-3|(-1x^2 - 2x + 1) - 3| + 2)) + 1) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3|(-5(1|(5(2cos(3\u03c0x - 2))^2 - 2(2cos(3\u03c0x - 2)) + 1) - 2| + 2) + 5) - 1| + 1 and g(x) = 2((3(-1|(-2x + 1) - 1| + 2) + 3)/(-3(-1|(-2x + 1) - 1| + 2))) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2|(-3|(4(-4(4x - 2) + 5) + 3)| - 3) + 2| - 2 and g(x) = -2|(3|(1((2x - 2)/(2x - 3))^2 - 1((2x - 2)/(2x - 3)) - 3) + 2|) - 1| + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(3|((-3(-1(2x - 2)^2 - 3(2x - 2) - 3) + 2)/(-1(-1(2x - 2)^2 - 3(2x - 2) - 3) + 3)) - 1| - 3)^2 - 4(3|((-3(-1(2x - 2)^2 - 3(2x - 2) - 3) + 2)/(-1(-1(2x - 2)^2 - 3(2x - 2) - 3) + 3)) - 1| - 3) - 5 and g(x) = 5(-1e^(-1((1(-4x^2 - 5x))/(1(-4x^2 - 5x) + 2))) + 3)^2 + 3(-1e^(-1((1(-4x^2 - 5x))/(1(-4x^2 - 5x) + 2))) + 3) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 4(5(-2(-2|(1|x - 3| + 1)|) - 5) - 4) + 5 and g(x) = (-3(5(2sin(2\u03c0((2x - 3)/(3x)) - 3) - 3) - 1) - 3)/(-1(5(2sin(2\u03c0((2x - 3)/(3x)) - 3) - 3) - 1) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 2(-1((1((3((1x - 3)/(1x + 3)) - 1)/(2((1x - 3)/(1x + 3)))) - 1)/(3((3((1x - 3)/(1x + 3)) - 1)/(2((1x - 3)/(1x + 3)))) - 2)) + 1) - 2 and g(x) = -4(1(1(5x + 4) - 3)^2 + 2(1(5x + 4) - 3) - 1) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3cos(1\u03c0((1(1|(-1|(-2x - 5) + 1| - 1) + 1| - 2))/(-3(1|(-1|(-2x - 5) + 1| - 1) + 1| - 2) + 2)) - 1) + 3 and g(x) = -2e^(-1(1(3((-1x + 3)/(2x + 1)) + 2) - 5)) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 3|((-1((-1(-1sin(1\u03c0(-2x) + 3) - 2) + 3)/(-2(-1sin(1\u03c0(-2x) + 3) - 2) - 2)))/(-3((-1(-1sin(1\u03c0(-2x) + 3) - 2) + 3)/(-2(-1sin(1\u03c0(-2x) + 3) - 2) - 2)) + 4)) + 2| - 3 and g(x) = (1((-3(2|(-4x - 2) - 1|))/(1(2|(-4x - 2) - 1|) - 2)) + 1)/(-1((-3(2|(-4x - 2) - 1|))/(1(2|(-4x - 2) - 1|) - 2)) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2((3((3(2|((-2x - 2)/(-2x)) + 3| - 3) + 2)/(2(2|((-2x - 2)/(-2x)) + 3| - 3) - 3)) - 2)/(2((3(2|((-2x - 2)/(-2x)) + 3| - 3) + 2)/(2(2|((-2x - 2)/(-2x)) + 3| - 3) - 3)) - 1)) - 4 and g(x) = 1sin(1\u03c0(-2(3(2x^2 - 3x + 1)^2 - 1(2x^2 - 3x + 1) + 2) - 5)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(2(-4((-2(-2|x + 3| - 3) - 1)/(-2(-2|x + 3| - 3) + 3))^2 - 1((-2(-2|x + 3| - 3) - 1)/(-2(-2|x + 3| - 3) + 3)) + 3)^2 + 1(-4((-2(-2|x + 3| - 3) - 1)/(-2(-2|x + 3| - 3) + 3))^2 - 1((-2(-2|x + 3| - 3) - 1)/(-2(-2|x + 3| - 3) + 3)) + 3) - 2) - 2)/(2(2(-4((-2(-2|x + 3| - 3) - 1)/(-2(-2|x + 3| - 3) + 3))^2 - 1((-2(-2|x + 3| - 3) - 1)/(-2(-2|x + 3| - 3) + 3)) + 3)^2 + 1(-4((-2(-2|x + 3| - 3) - 1)/(-2(-2|x + 3| - 3) + 3))^2 - 1((-2(-2|x + 3| - 3) - 1)/(-2(-2|x + 3| - 3) + 3)) + 3) - 2) + 1) and g(x) = -4((1((-3(-4x + 3) - 2)/(-3(-4x + 3) + 1)) - 2)/(-1((-3(-4x + 3) - 2)/(-3(-4x + 3) + 1)) + 2)) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 3(4((-2((1(2x + 3) + 3)/(2(2x + 3) + 1)) - 1)/(-1((1(2x + 3) + 3)/(2(2x + 3) + 1)) + 2))^2 - 4((-2((1(2x + 3) + 3)/(2(2x + 3) + 1)) - 1)/(-1((1(2x + 3) + 3)/(2(2x + 3) + 1)) + 2)) + 4) + 2 and g(x) = (-2(-2e^(-1((3(2x^2 - 3x - 2) - 2)/(1(2x^2 - 3x - 2) + 1))) + 1) + 2)/(2(-2e^(-1((3(2x^2 - 3x - 2) - 2)/(1(2x^2 - 3x - 2) + 1))) + 1) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (-3((-1(1(-1((-3x - 1)/(-1x - 1)) - 5)^2 + 2(-1((-3x - 1)/(-1x - 1)) - 5)) - 2)/(-2(1(-1((-3x - 1)/(-1x - 1)) - 5)^2 + 2(-1((-3x - 1)/(-1x - 1)) - 5)) - 1)) - 2)/(-2((-1(1(-1((-3x - 1)/(-1x - 1)) - 5)^2 + 2(-1((-3x - 1)/(-1x - 1)) - 5)) - 2)/(-2(1(-1((-3x - 1)/(-1x - 1)) - 5)^2 + 2(-1((-3x - 1)/(-1x - 1)) - 5)) - 1)) + 3) and g(x) = 3(-2|((2((1x + 1)/(-3x - 1)) - 3)/(-3((1x + 1)/(-3x - 1)) + 2))| + 3) + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(-2|((1(-3cos(1\u03c0(-1x + 1) - 1) + 2) + 2)/(1(-3cos(1\u03c0(-1x + 1) - 1) + 2) + 2)) + 3| + 1) - 1 and g(x) = 1((1(-1(-3|x + 1| - 3)) - 1)/(1(-1(-3|x + 1| - 3)) - 3)) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (2(3(3(5((-2x + 2)/(-2x + 3)) + 4)^2 - 3(5((-2x + 2)/(-2x + 3)) + 4) + 3) - 2) - 3)/(-3(3(3(5((-2x + 2)/(-2x + 3)) + 4)^2 - 3(5((-2x + 2)/(-2x + 3)) + 4) + 3) - 2) + 1) and g(x) = -3|(2|(3(3x - 3)^2 + 5(3x - 3) + 2) + 1|) - 1| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 5(1(2|((3((2x + 3)/(-3x - 2)) + 1)/(2((2x + 3)/(-3x - 2)) + 2)) + 2| + 1)^2 - 2(2|((3((2x + 3)/(-3x - 2)) + 1)/(2((2x + 3)/(-3x - 2)) + 2)) + 2| + 1) + 3) - 5 and g(x) = 1((2(-2cos(1\u03c0((3x + 3)/(1x - 3)) - 1) - 3) - 2)/(-2(-2cos(1\u03c0((3x + 3)/(1x - 3)) - 1) - 3) + 3))^2 + 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -4((2(-3(-1(-1x + 5) - 4) - 3) + 3)/(-1(-3(-1(-1x + 5) - 4) - 3) - 3)) - 4 and g(x) = -5((-3(-3e^(-1((1x - 2)/(2x + 3))) + 1) + 1)/(-1(-3e^(-1((1x - 2)/(2x + 3))) + 1) + 2)) + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|((-3(-3cos(2\u03c0(-2|(1x^2 + 1x + 5) + 1| + 3) + 1) + 1) + 3)/(-2(-3cos(2\u03c0(-2|(1x^2 + 1x + 5) + 1| + 3) + 1) + 1) + 3)) - 2| - 1 and g(x) = (-3(2e^(-2(-5(2|x - 1| - 1) + 2)) - 1) + 1)/(-3(2e^(-2(-5(2|x - 1| - 1) + 2)) - 1) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(3|(1(2(2cos(2\u03c0x - 1) + 2)^2 - 4(2cos(2\u03c0x - 1) + 2) + 3) + 4)| - 2)^2 - 5(3|(1(2(2cos(2\u03c0x - 1) + 2)^2 - 4(2cos(2\u03c0x - 1) + 2) + 3) + 4)| - 2) + 1 and g(x) = -1|(-2|(-3((3x + 1)/(1x + 1)) + 5) + 3| + 2) + 3| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3e^(-2((2((-1(1(1x^2 + 1x + 1)^2 + 3) - 3)/(-1(1(1x^2 + 1x + 1)^2 + 3) - 2)) + 2)/(3((-1(1(1x^2 + 1x + 1)^2 + 3) - 3)/(-1(1(1x^2 + 1x + 1)^2 + 3) - 2)) + 1))) - 2 and g(x) = -4(-4(1((-2x)/(-1x - 1)) + 2) - 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3|(-2(-2|(2|((-1x)/(3x + 3)) - 3| + 2) + 3| + 2)^2 - 4(-2|(2|((-1x)/(3x + 3)) - 3| + 2) + 3| + 2) + 4) + 2| + 1 and g(x) = -3(1(-3(-3x + 3)^2 + 4(-3x + 3) + 2)^2 + 2(-3(-3x + 3)^2 + 4(-3x + 3) + 2) - 3)^2 - 5(1(-3(-3x + 3)^2 + 4(-3x + 3) + 2)^2 + 2(-3(-3x + 3)^2 + 4(-3x + 3) + 2) - 3) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1|(-3(-1|((1((2x - 3)/(-2x)) + 1)/(3((2x - 3)/(-2x)) + 3)) + 1| - 1) + 5) + 2| + 1 and g(x) = 1(2|((-3(2x - 5) - 1)/(-2(2x - 5) + 1)) - 2| - 1)^2 + 2(2|((-3(2x - 5) - 1)/(-2(2x - 5) + 1)) - 2| - 1) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3(-1((-2(-3(-1|x + 2| + 3) + 1) + 1)/(2(-3(-1|x + 2| + 3) + 1) + 2)) - 2) - 2 and g(x) = -3(2((-1((-1x)/(-1x + 2)) - 1)/(-2((-1x)/(-1x + 2)) - 1)) - 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1(3|((2(-4(2|x - 3| + 1) + 4) - 2)/(-1(-4(2|x - 3| + 1) + 4) + 2)) - 2| - 2) - 4 and g(x) = -2|(2e^(2(-3((3x + 1)/(1x - 2)) + 3)) - 2) + 3| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (3(2|(-4(-3((-2x + 3)/(2x + 2)) - 5) - 2) - 3| - 3))/(3(2|(-4(-3((-2x + 3)/(2x + 2)) - 5) - 2) - 3| - 3) - 1) and g(x) = -4(2sin(2\u03c0(-4((3x + 1)/(-3x + 4))^2 + 5((3x + 1)/(-3x + 4)) + 3) + 2) + 3) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 5(-1|((-1(-3|(2cos(1\u03c0x + 3) - 3) - 1| + 1) - 1)/(-1(-3|(2cos(1\u03c0x + 3) - 3) - 1| + 1) - 3)) - 3| - 1) + 2 and g(x) = -2((-1((-2((1x + 3)/(2x - 3)) - 2)/(-1((1x + 3)/(2x - 3)) + 3)) + 2)/(-2((-2((1x + 3)/(2x - 3)) - 2)/(-1((1x + 3)/(2x - 3)) + 3)) + 3))^2 + 1((-1((-2((1x + 3)/(2x - 3)) - 2)/(-1((1x + 3)/(2x - 3)) + 3)) + 2)/(-2((-2((1x + 3)/(2x - 3)) - 2)/(-1((1x + 3)/(2x - 3)) + 3)) + 3)) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 5(-2(-1(-3|(4x^2 - 1x + 3) - 2| - 1) + 1))^2 + 3(-2(-1(-3|(4x^2 - 1x + 3) - 2| - 1) + 1)) - 5 and g(x) = 1|(-2|(-2e^(-1(4x - 4)) - 3) + 3| - 2) + 3| - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3(2(1(1sin(1\u03c0((-3x - 3)/(-1x + 3)) - 3) + 3)^2 + 3(1sin(1\u03c0((-3x - 3)/(-1x + 3)) - 3) + 3) - 5)^2 - 2(1(1sin(1\u03c0((-3x - 3)/(-1x + 3)) - 3) + 3)^2 + 3(1sin(1\u03c0((-3x - 3)/(-1x + 3)) - 3) + 3) - 5) - 3)^2 - 4(2(1(1sin(1\u03c0((-3x - 3)/(-1x + 3)) - 3) + 3)^2 + 3(1sin(1\u03c0((-3x - 3)/(-1x + 3)) - 3) + 3) - 5)^2 - 2(1(1sin(1\u03c0((-3x - 3)/(-1x + 3)) - 3) + 3)^2 + 3(1sin(1\u03c0((-3x - 3)/(-1x + 3)) - 3) + 3) - 5) - 3) + 4 and g(x) = 1(4((-3(2x^2 + 2x - 3) + 1)/(3(2x^2 + 2x - 3) + 1))^2 - 5((-3(2x^2 + 2x - 3) + 1)/(3(2x^2 + 2x - 3) + 1)) + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2(-5(-3e^(2(4((2x - 2)/(2x + 2)) - 5)) - 1)^2 - 4(-3e^(2(4((2x - 2)/(2x + 2)) - 5)) - 1) + 2) - 1 and g(x) = 2(-5(1e^(-1(-3x - 1)) - 3)^2 + 4(1e^(-1(-3x - 1)) - 3) + 1) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-9", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1(-2(-3sin(2\u03c0(-2|(1|x| + 2) + 1| + 3) + 2) + 1) + 2)^2 + 3 and g(x) = -5((2(5(-5x + 2)^2 - 4(-5x + 2) - 5) - 1)/(1(5(-5x + 2)^2 - 4(-5x + 2) - 5) - 3)) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5((2(1(3(-2|x - 3| + 1) + 2) - 1))/(1(1(3(-2|x - 3| + 1) + 2) - 1) + 1)) + 4 and g(x) = 2|(-1|(-1(-2e^(1x) - 3) + 3) - 3| - 1) - 2| intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 4(5((3((-3((2x + 1)/(-3x + 2)))/(-3((2x + 1)/(-3x + 2)) + 2)) + 1)/(-1((-3((2x + 1)/(-3x + 2)))/(-3((2x + 1)/(-3x + 2)) + 2)) + 2)) - 2) and g(x) = -1((3(3|(-4x) + 3| - 3) - 3)/(-2(3|(-4x) + 3| - 3))) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1(-4(2cos(1\u03c0((-2(1|x| + 2))/(1(1|x| + 2) + 2)) - 1) + 2) - 4)^2 + 1 and g(x) = -1|((2(-1(-1x + 1) - 2) - 2)/(3(-1(-1x + 1) - 2) - 2)) + 1| - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5((-2((-1(-1|(-1x^2 + 3x - 3)| - 2))/(3(-1|(-1x^2 + 3x - 3)| - 2) + 3)) + 1)/(-2((-1(-1|(-1x^2 + 3x - 3)| - 2))/(3(-1|(-1x^2 + 3x - 3)| - 2) + 3)) - 3))^2 + 4((-2((-1(-1|(-1x^2 + 3x - 3)| - 2))/(3(-1|(-1x^2 + 3x - 3)| - 2) + 3)) + 1)/(-2((-1(-1|(-1x^2 + 3x - 3)| - 2))/(3(-1|(-1x^2 + 3x - 3)| - 2) + 3)) - 3)) + 5 and g(x) = -2|(-2(-2e^(1(-4x + 2)) + 2)^2 + 1(-2e^(1(-4x + 2)) + 2) + 2) + 3| + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3((-1((-1((-2(-1|x + 3|))/(-2(-1|x + 3|) + 1)) + 2)/(-2((-2(-1|x + 3|))/(-2(-1|x + 3|) + 1)))) - 1)/(-3((-1((-2(-1|x + 3|))/(-2(-1|x + 3|) + 1)) + 2)/(-2((-2(-1|x + 3|))/(-2(-1|x + 3|) + 1)))) - 1)) + 2 and g(x) = (1(-2((-1((-1x + 1)/(2x + 1)) - 3)/(1((-1x + 1)/(2x + 1)) + 1)) + 1) + 3)/(2(-2((-1((-1x + 1)/(2x + 1)) - 3)/(1((-1x + 1)/(2x + 1)) + 1)) + 1) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 5((3(4(1(-3|x - 3| + 2)^2 - 1(-3|x - 3| + 2) - 3) - 1) + 2)/(-2(4(1(-3|x - 3| + 2)^2 - 1(-3|x - 3| + 2) - 3) - 1) - 2)) and g(x) = (1(-5(-3|((-2x - 2)/(3x + 3)) - 2|)^2 - 2(-3|((-2x - 2)/(3x + 3)) - 2|) - 5) + 2)/(1(-5(-3|((-2x - 2)/(3x + 3)) - 2|)^2 - 2(-3|((-2x - 2)/(3x + 3)) - 2|) - 5) + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-1((-2(4((-1(-4x))/(-1(-4x) + 2))^2 + 1((-1(-4x))/(-1(-4x) + 2)) - 1) - 2)/(-2(4((-1(-4x))/(-1(-4x) + 2))^2 + 1((-1(-4x))/(-1(-4x) + 2)) - 1) + 3)) + 3)/(2((-2(4((-1(-4x))/(-1(-4x) + 2))^2 + 1((-1(-4x))/(-1(-4x) + 2)) - 1) - 2)/(-2(4((-1(-4x))/(-1(-4x) + 2))^2 + 1((-1(-4x))/(-1(-4x) + 2)) - 1) + 3)) - 1) and g(x) = -1e^(-1(5(4(-5x + 4) - 2)^2 + 5(4(-5x + 4) - 2) - 3)) - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1(-4((-2(-2sin(1\u03c0(-3|x - 3| - 1)) + 3) + 1)/(-3(-2sin(1\u03c0(-3|x - 3| - 1)) + 3) - 3)) + 5) + 3)/(1(-4((-2(-2sin(1\u03c0(-3|x - 3| - 1)) + 3) + 1)/(-3(-2sin(1\u03c0(-3|x - 3| - 1)) + 3) - 3)) + 5)) and g(x) = 4(3(-3e^(-1(-1x + 2)) - 1) + 4) + 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1(3(-3(1(-2|x + 3| + 3)^2 + 4(-2|x + 3| + 3) + 2)^2 + 3(1(-2|x + 3| + 3)^2 + 4(-2|x + 3| + 3) + 2) - 4) + 3) + 2)/(3(3(-3(1(-2|x + 3| + 3)^2 + 4(-2|x + 3| + 3) + 2)^2 + 3(1(-2|x + 3| + 3)^2 + 4(-2|x + 3| + 3) + 2) - 4) + 3) + 1) and g(x) = -1|((-3(-4((3x + 3)/(-1x - 2)) + 4) + 3)/(2(-4((3x + 3)/(-1x - 2)) + 4) + 1)) - 2| meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 5(2|((-3(1|((-1x + 2)/(1x + 3))| - 3) - 1)/(2(1|((-1x + 2)/(1x + 3))| - 3) + 2)) + 1| - 2)^2 - 3(2|((-3(1|((-1x + 2)/(1x + 3))| - 3) - 1)/(2(1|((-1x + 2)/(1x + 3))| - 3) + 2)) + 1| - 2) + 5 and g(x) = 3(-2(-5((-1x)/(-1x - 3))) + 1) + 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(-3(-3(-5(-4x + 4) - 2) - 3) - 4) - 2)/(3(-3(-3(-5(-4x + 4) - 2) - 3) - 4) + 2) and g(x) = 4((-1(-2|(1x - 5) - 1| + 3) - 3)/(2(-2|(1x - 5) - 1| + 3) + 3)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2|(1((-1(5(3x + 5) - 1) + 2)/(3(5(3x + 5) - 1) - 2))^2 + 4((-1(5(3x + 5) - 1) + 2)/(3(5(3x + 5) - 1) - 2)) + 3) + 3| + 2 and g(x) = (3(4(2(-3cos(2\u03c0x - 2) - 1) - 1) - 3) + 2)/(3(4(2(-3cos(2\u03c0x - 2) - 1) - 1) - 3) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -3((-2(5(-1sin(1\u03c0(-2x^2 - 3x - 5) + 3) - 3)^2 - 1(-1sin(1\u03c0(-2x^2 - 3x - 5) + 3) - 3) - 3) - 1)/(-2(5(-1sin(1\u03c0(-2x^2 - 3x - 5) + 3) - 3)^2 - 1(-1sin(1\u03c0(-2x^2 - 3x - 5) + 3) - 3) - 3) - 1))^2 + 3((-2(5(-1sin(1\u03c0(-2x^2 - 3x - 5) + 3) - 3)^2 - 1(-1sin(1\u03c0(-2x^2 - 3x - 5) + 3) - 3) - 3) - 1)/(-2(5(-1sin(1\u03c0(-2x^2 - 3x - 5) + 3) - 3)^2 - 1(-1sin(1\u03c0(-2x^2 - 3x - 5) + 3) - 3) - 3) - 1)) - 1 and g(x) = (-3((1((-1(1x^2 + 2x - 3) - 1)/(-3(1x^2 + 2x - 3) + 1)) - 2)/(-2((-1(1x^2 + 2x - 3) - 1)/(-3(1x^2 + 2x - 3) + 1)) + 3)) + 3)/(-3((1((-1(1x^2 + 2x - 3) - 1)/(-3(1x^2 + 2x - 3) + 1)) - 2)/(-2((-1(1x^2 + 2x - 3) - 1)/(-3(1x^2 + 2x - 3) + 1)) + 3)) + 1) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (1((-2(5(-1(-3x^2 + 1x + 4) - 1)^2 + 1(-1(-3x^2 + 1x + 4) - 1) - 1) - 3)/(-3(5(-1(-3x^2 + 1x + 4) - 1)^2 + 1(-1(-3x^2 + 1x + 4) - 1) - 1) - 2)) - 3)/(2((-2(5(-1(-3x^2 + 1x + 4) - 1)^2 + 1(-1(-3x^2 + 1x + 4) - 1) - 1) - 3)/(-3(5(-1(-3x^2 + 1x + 4) - 1)^2 + 1(-1(-3x^2 + 1x + 4) - 1) - 1) - 2)) - 1) and g(x) = 3(5(1(1e^(-1x) + 2) - 4) + 2) + 1 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 5(3((-2(-3e^(1((1x)/(-1x - 3))) + 1))/(-2(-3e^(1((1x)/(-1x - 3))) + 1) - 2))^2 + 4((-2(-3e^(1((1x)/(-1x - 3))) + 1))/(-2(-3e^(1((1x)/(-1x - 3))) + 1) - 2)) - 2)^2 - 4(3((-2(-3e^(1((1x)/(-1x - 3))) + 1))/(-2(-3e^(1((1x)/(-1x - 3))) + 1) - 2))^2 + 4((-2(-3e^(1((1x)/(-1x - 3))) + 1))/(-2(-3e^(1((1x)/(-1x - 3))) + 1) - 2)) - 2) + 5 and g(x) = 2|(1(-2(1e^(-2x) + 3) + 1) - 4) + 2| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 5((3(-2|(-2(2|x| + 1)^2 - 2(2|x| + 1) + 3) - 1| - 1) + 2)/(-3(-2|(-2(2|x| + 1)^2 - 2(2|x| + 1) + 3) - 1| - 1) - 2))^2 + 2((3(-2|(-2(2|x| + 1)^2 - 2(2|x| + 1) + 3) - 1| - 1) + 2)/(-3(-2|(-2(2|x| + 1)^2 - 2(2|x| + 1) + 3) - 1| - 1) - 2)) + 3 and g(x) = 4(-1(-1(-2x^2 + 5x - 4)^2 - 4(-2x^2 + 5x - 4) - 2) - 2) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3(-2|(2(-5(-4x + 4) + 1) + 2) - 3|)^2 - 3 and g(x) = -2((1(1|(-3cos(1\u03c0x - 1) - 1) - 2| - 1) + 2)/(3(1|(-3cos(1\u03c0x - 1) - 1) - 2| - 1))) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4(1|(-1|(-2((-3x - 3)/(2x)) + 5) + 2| - 2)| - 1) - 1 and g(x) = -3(3(2(3|x - 3| - 1) + 4)^2 + 3(2(3|x - 3| - 1) + 4) - 5) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-3(2(5((-3(1|x + 2| - 3) - 1)/(-2(1|x + 2| - 3) - 1))^2 + 5((-3(1|x + 2| - 3) - 1)/(-2(1|x + 2| - 3) - 1)) - 3)^2 + 3(5((-3(1|x + 2| - 3) - 1)/(-2(1|x + 2| - 3) - 1))^2 + 5((-3(1|x + 2| - 3) - 1)/(-2(1|x + 2| - 3) - 1)) - 3) - 5) + 3)/(2(2(5((-3(1|x + 2| - 3) - 1)/(-2(1|x + 2| - 3) - 1))^2 + 5((-3(1|x + 2| - 3) - 1)/(-2(1|x + 2| - 3) - 1)) - 3)^2 + 3(5((-3(1|x + 2| - 3) - 1)/(-2(1|x + 2| - 3) - 1))^2 + 5((-3(1|x + 2| - 3) - 1)/(-2(1|x + 2| - 3) - 1)) - 3) - 5) - 1) and g(x) = -1(-1|(-1((-2x + 3)/(1x + 2))^2 - 4((-2x + 3)/(1x + 2)) + 4) - 3| + 1)^2 - 4(-1|(-1((-2x + 3)/(1x + 2))^2 - 4((-2x + 3)/(1x + 2)) + 4) - 3| + 1) + 4 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-2(1|(5(-5(2e^(-1x) - 3)^2 - 4) - 4) + 1| + 3) + 2)/(2(1|(5(-5(2e^(-1x) - 3)^2 - 4) - 4) + 1| + 3) + 3) and g(x) = 1(-2|((3(-3x - 3) - 3)/(-1(-3x - 3) + 2)) + 1| + 1) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -5((2(2(-2(-3x^2 - 2x - 3) + 1)^2 - 2(-2(-3x^2 - 2x - 3) + 1) + 1) - 1)/(2(2(-2(-3x^2 - 2x - 3) + 1)^2 - 2(-2(-3x^2 - 2x - 3) + 1) + 1) - 1))^2 - 4((2(2(-2(-3x^2 - 2x - 3) + 1)^2 - 2(-2(-3x^2 - 2x - 3) + 1) + 1) - 1)/(2(2(-2(-3x^2 - 2x - 3) + 1)^2 - 2(-2(-3x^2 - 2x - 3) + 1) + 1) - 1)) + 4 and g(x) = -2|(2((-3(-4x - 3) + 3)/(2(-4x - 3) - 1)) - 3) + 3| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (2((-1(-2(-3(3x + 4)^2 + 5(3x + 4) + 2) - 2) + 3)/(-3(-2(-3(3x + 4)^2 + 5(3x + 4) + 2) - 2) + 1)) - 1)/(1((-1(-2(-3(3x + 4)^2 + 5(3x + 4) + 2) - 2) + 3)/(-3(-2(-3(3x + 4)^2 + 5(3x + 4) + 2) - 2) + 1))) and g(x) = -1|(4(2cos(1\u03c0(-2x - 3) - 1) - 2)^2 + 4(2cos(1\u03c0(-2x - 3) - 1) - 2) + 1) - 1| - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 5((-3(-2e^(2(1|(3x + 5) + 3| - 2)) - 3) - 2)/(3(-2e^(2(1|(3x + 5) + 3| - 2)) - 3) - 2))^2 + 2((-3(-2e^(2(1|(3x + 5) + 3| - 2)) - 3) - 2)/(3(-2e^(2(1|(3x + 5) + 3| - 2)) - 3) - 2)) - 5 and g(x) = (-3((2(5((-3x - 1)/(-3x)) - 2) + 3)/(-2(5((-3x - 1)/(-3x)) - 2))) - 2)/(-2((2(5((-3x - 1)/(-3x)) - 2) + 3)/(-2(5((-3x - 1)/(-3x)) - 2))) + 1) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (1(-1(4((3(3x - 2) - 2)/(-1(3x - 2) + 3))^2 + 2)^2 + 3(4((3(3x - 2) - 2)/(-1(3x - 2) + 3))^2 + 2)) - 3)/(3(-1(4((3(3x - 2) - 2)/(-1(3x - 2) + 3))^2 + 2)^2 + 3(4((3(3x - 2) - 2)/(-1(3x - 2) + 3))^2 + 2)) - 2) and g(x) = 3(-2(-1cos(3\u03c0(-2x - 1) - 2) + 3) + 3) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-2(5(3|(4((3x - 1)/(-1x + 3)) + 5) + 2| - 1) + 2))/(-2(5(3|(4((3x - 1)/(-1x + 3)) + 5) + 2| - 1) + 2) - 1) and g(x) = (2(-2|(-1(-2|x + 3| - 1) + 1)|))/(-2(-2|(-1(-2|x + 3| - 1) + 1)|) - 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 1((-3(3e^(1(3((-2x + 2)/(-2x + 3))^2 + 3((-2x + 2)/(-2x + 3)) - 3)) - 2) - 3)/(2(3e^(1(3((-2x + 2)/(-2x + 3))^2 + 3((-2x + 2)/(-2x + 3)) - 3)) - 2) + 1)) + 3 and g(x) = (3((1(3|(-5x^2 + 2x + 2) - 2| - 1) + 3)/(1(3|(-5x^2 + 2x + 2) - 2| - 1) + 2)) + 3)/(-3((1(3|(-5x^2 + 2x + 2) - 2| - 1) + 3)/(1(3|(-5x^2 + 2x + 2) - 2| - 1) + 2))) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3(-1(2(-2(-3x^2 + 2x + 2) - 4) + 2) + 5) + 5 and g(x) = -1|(-1|(2(1|x - 2| + 1) - 3) + 2|) - 1| + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(-1|(-1sin(2\u03c0(3(1x^2 + 2x - 4) - 1) - 3) + 2) + 2|) - 2 and g(x) = 5(-1((-3(1e^(-2x) - 3) + 2)/(1(1e^(-2x) - 3) + 2)) + 2)^2 + 5(-1((-3(1e^(-2x) - 3) + 2)/(1(1e^(-2x) - 3) + 2)) + 2) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (2(-2|(3((-2(-2x))/(-3(-2x)))^2 - 1((-2(-2x))/(-3(-2x))) - 1)| + 2))/(-1(-2|(3((-2(-2x))/(-3(-2x)))^2 - 1((-2(-2x))/(-3(-2x))) - 1)| + 2) - 3) and g(x) = -4((2(2e^(-2((-2x + 2)/(1x))) - 3))/(3(2e^(-2((-2x + 2)/(1x))) - 3) - 2)) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1|((-1(2(3((-3x + 3)/(-3x + 4)) + 4) - 3) + 2)/(1(2(3((-3x + 3)/(-3x + 4)) + 4) - 3) - 3)) - 2| and g(x) = 3|(-2cos(3\u03c0(2(2|x - 1| + 3)^2 - 1(2|x - 1| + 3) + 2)) + 3)| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -3(-3(-5(2(4x - 4) + 5) - 2) - 1)^2 - 3(-3(-5(2(4x - 4) + 5) - 2) - 1) - 2 and g(x) = -2|(-3|(5(4x^2 - 3x - 4)^2 - 4(4x^2 - 3x - 4) + 2) + 3| - 1) + 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (3(1|(-3|((-3(5x^2 + 1x + 5) - 3)/(1(5x^2 + 1x + 5))) + 2| - 2) - 2| - 2) + 3)/(-2(1|(-3|((-3(5x^2 + 1x + 5) - 3)/(1(5x^2 + 1x + 5))) + 2| - 2) - 2| - 2) + 3) and g(x) = -3|(-1e^(1(1(-1x + 2) + 5)) + 2) + 1| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(4((-3(3|(1x + 2) - 3| + 2))/(2(3|(1x + 2) - 3| + 2) - 3)) + 2) + 3| - 3 and g(x) = -3e^(-1(3(-1(5x - 5)^2 - 2(5x - 5) + 3) - 5)) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -3|((2(-1|((-1((-1x + 3)/(-3x - 3)) + 2)/(-2((-1x + 3)/(-3x - 3))))| - 1) + 1)/(3(-1|((-1((-1x + 3)/(-3x - 3)) + 2)/(-2((-1x + 3)/(-3x - 3))))| - 1) - 2)) - 1| - 1 and g(x) = (-3((-1(-4(-1|x + 2| + 1)^2 + 3(-1|x + 2| + 1) - 1) - 3)/(1(-4(-1|x + 2| + 1)^2 + 3(-1|x + 2| + 1) - 1) - 3)) + 3)/(-2((-1(-4(-1|x + 2| + 1)^2 + 3(-1|x + 2| + 1) - 1) - 3)/(1(-4(-1|x + 2| + 1)^2 + 3(-1|x + 2| + 1) - 1) - 3)) - 1) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(3|(-1(-3(-5x + 1) - 3)^2 - 4(-3(-5x + 1) - 3) + 2)| - 1) + 3| and g(x) = 5(1(3|(-2x + 4) - 3| - 2)^2 - 5(3|(-2x + 4) - 3| - 2) - 1) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5(3|(3e^(2(-4(3|x|)^2 + 5(3|x|) - 4)) + 3)| + 3) - 5 and g(x) = 1(-2|((-3((-3x)/(-3x + 1)) - 2)/(3((-3x)/(-3x + 1)) - 2)) + 3| - 1) + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2(-3|(-1e^(1(-4(-2x^2 - 5x + 2) + 3))) - 1| - 3) and g(x) = (2(-2(-3e^(-1((2x - 2)/(-2x - 2))) + 1) + 1) - 3)/(3(-2(-3e^(-1((2x - 2)/(-2x - 2))) + 1) + 1) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 1((2(1((-1(-2|x + 3| - 3) + 3)/(2(-2|x + 3| - 3) + 3))^2 + 2((-1(-2|x + 3| - 3) + 3)/(2(-2|x + 3| - 3) + 3)) + 1) - 2)/(-2(1((-1(-2|x + 3| - 3) + 3)/(2(-2|x + 3| - 3) + 3))^2 + 2((-1(-2|x + 3| - 3) + 3)/(2(-2|x + 3| - 3) + 3)) + 1) + 1)) and g(x) = 1|(-3cos(3\u03c0(1|(1x - 4) + 3| - 2) - 2) + 1) + 2| meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (-1(-4(2|(-1|(-3x + 1) + 2|)| - 2)) - 2)/(-1(-4(2|(-1|(-3x + 1) + 2|)| - 2)) + 3) and g(x) = 3(-3(-4(3x^2 - 2x - 3) - 4) + 1) - 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1|(-3(3((-1(2cos(2\u03c0x - 3) - 3) - 1)/(2(2cos(2\u03c0x - 3) - 3))) + 3)^2 + 1(3((-1(2cos(2\u03c0x - 3) - 3) - 1)/(2(2cos(2\u03c0x - 3) - 3))) + 3) - 2) + 2| + 3 and g(x) = -1(2((1(4x - 3) + 3)/(1(4x - 3) + 2))^2 - 5((1(4x - 3) + 3)/(1(4x - 3) + 2)) - 5) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (2(2sin(2\u03c0(5((2(3|x - 2| + 3) + 1)/(-1(3|x - 2| + 3) - 1)) + 3) - 2) - 3) - 3)/(2(2sin(2\u03c0(5((2(3|x - 2| + 3) + 1)/(-1(3|x - 2| + 3) - 1)) + 3) - 2) - 3) - 1) and g(x) = 2|(-4(-2|(3e^(1x) - 2) + 2| + 1)^2 + 2(-2|(3e^(1x) - 2) + 2| + 1) + 4) - 1| - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 5(-4((-2(-5((-2x)/(1x + 2))) - 2)/(-2(-5((-2x)/(1x + 2))) + 3)) + 4) - 2 and g(x) = 4(-1|(5(-1x - 1)^2 - 2(-1x - 1) + 1)| - 2) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(-1|(-1(4((3x)/(-1x - 1))^2 - 3((3x)/(-1x - 1))) - 2) - 1| + 1) + 4 and g(x) = -1(1|(-3(-5x - 3)^2 - 5(-5x - 3) + 5)|) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3((-3(1(-1((-1x + 1)/(-3x + 4))^2 - 3((-1x + 1)/(-3x + 4)) - 1) + 5) + 2)/(-1(1(-1((-1x + 1)/(-3x + 4))^2 - 3((-1x + 1)/(-3x + 4)) - 1) + 5) + 2)) - 4 and g(x) = (-2((1(1(-2e^(-2x) + 3) - 5) + 2)/(1(1(-2e^(-2x) + 3) - 5) + 2)) + 1)/(3((1(1(-2e^(-2x) + 3) - 5) + 2)/(1(1(-2e^(-2x) + 3) - 5) + 2)) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1(-4(-1(3cos(3\u03c0(-1|x - 1| + 2) - 1) + 3) - 2) - 3) + 5 and g(x) = 3(-2(-1(-5x + 4)^2 - 5(-5x + 4) - 1) + 2) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 1(-2(-5(3e^(-1(-2|x| + 2)) - 1)^2 - 4)^2 - 5(-5(3e^(-1(-2|x| + 2)) - 1)^2 - 4) - 5)^2 - 3(-2(-5(3e^(-1(-2|x| + 2)) - 1)^2 - 4)^2 - 5(-5(3e^(-1(-2|x| + 2)) - 1)^2 - 4) - 5) - 2 and g(x) = 2(3|(-3(1|x + 3| + 1)^2 - 2(1|x + 3| + 1) - 2) + 3|)^2 - 4(3|(-3(1|x + 3| + 1)^2 - 2(1|x + 3| + 1) - 2) + 3|) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-2((-3((-1(2e^(-1((-1x - 1)/(3x - 2))) - 2) + 3)/(-2(2e^(-1((-1x - 1)/(3x - 2))) - 2) + 3)) - 1)/(-2((-1(2e^(-1((-1x - 1)/(3x - 2))) - 2) + 3)/(-2(2e^(-1((-1x - 1)/(3x - 2))) - 2) + 3)) - 2)) + 2)/(2((-3((-1(2e^(-1((-1x - 1)/(3x - 2))) - 2) + 3)/(-2(2e^(-1((-1x - 1)/(3x - 2))) - 2) + 3)) - 1)/(-2((-1(2e^(-1((-1x - 1)/(3x - 2))) - 2) + 3)/(-2(2e^(-1((-1x - 1)/(3x - 2))) - 2) + 3)) - 2)) - 1) and g(x) = -3|((1(-2|(3x^2 + 2x + 4)| - 3) - 1)/(-1(-2|(3x^2 + 2x + 4)| - 3) + 2)) + 2| intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3|(-4(-5(-3(-3|x + 2| - 1) - 4)^2 - 1(-3(-3|x + 2| - 1) - 4) + 3) - 4) - 3| - 1 and g(x) = -3((2(3(-2x^2 - 4x - 2)^2 + 1(-2x^2 - 4x - 2) - 2) + 2)/(-1(3(-2x^2 - 4x - 2)^2 + 1(-2x^2 - 4x - 2) - 2) + 2)) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1sin(3\u03c0(-3|(3((1(2|x - 3| + 2) - 2)/(-1(2|x - 3| + 2) - 3)) + 3) - 3| + 3)) + 2 and g(x) = 4((1((1(-5x^2 - 3x - 4))/(-1(-5x^2 - 3x - 4) - 1)) + 1)/(-2((1(-5x^2 - 3x - 4))/(-1(-5x^2 - 3x - 4) - 1)) - 3)) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5(2(1((-1(3|x + 2| + 3) + 1)/(-1(3|x + 2| + 3) + 2))^2 + 2((-1(3|x + 2| + 3) + 1)/(-1(3|x + 2| + 3) + 2)) - 5) - 4)^2 + 1(2(1((-1(3|x + 2| + 3) + 1)/(-1(3|x + 2| + 3) + 2))^2 + 2((-1(3|x + 2| + 3) + 1)/(-1(3|x + 2| + 3) + 2)) - 5) - 4) - 5 and g(x) = -1e^(-1((-2(-3(5x^2 - 5x - 2) - 3) + 2)/(-2(-3(5x^2 - 5x - 2) - 3) - 2))) - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (1(-3(2e^(-2((2(-3x^2 + 5x - 1) + 1)/(-1(-3x^2 + 5x - 1) - 3))) - 1) + 5) - 3)/(-3(-3(2e^(-2((2(-3x^2 + 5x - 1) + 1)/(-1(-3x^2 + 5x - 1) - 3))) - 1) + 5) + 2) and g(x) = -2(4((-1(-4x + 5))/(2(-4x + 5))) + 4) + 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -3((-1(1sin(1\u03c0(1|(5x^2 - 5x + 5) - 1| - 2) - 1) - 3) - 2)/(3(1sin(1\u03c0(1|(5x^2 - 5x + 5) - 1| - 2) - 1) - 3) + 3))^2 + 5 and g(x) = 1((-2(-4(-3e^(-1x) + 1) - 2) - 2)/(-2(-4(-3e^(-1x) + 1) - 2)))^2 - 5((-2(-4(-3e^(-1x) + 1) - 2) - 2)/(-2(-4(-3e^(-1x) + 1) - 2))) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (3((1(-4(-2(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 4)^2 - 3(-2(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 4) - 2) + 3)/(-1(-4(-2(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 4)^2 - 3(-2(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 4) - 2) + 2)) + 1)/(-1((1(-4(-2(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 4)^2 - 3(-2(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 4) - 2) + 3)/(-1(-4(-2(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 4)^2 - 3(-2(-1|x + 2| + 1)^2 - 1(-1|x + 2| + 1) - 4) - 2) + 2)) - 3) and g(x) = 1(-1(-1((2x + 3)/(-3x)) + 2) - 5)^2 - 5(-1(-1((2x + 3)/(-3x)) + 2) - 5) - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3|(5(-2e^(-1(2|(-1x - 5)|)) - 1)^2 + 2(-2e^(-1(2|(-1x - 5)|)) - 1) - 5) - 1| - 2 and g(x) = 2(-1|(-1|(5x^2 + 1x - 1) + 2| + 2) + 3| + 2) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3sin(2\u03c0(2|(5(4(5x^2 - 2)^2 - 2(5x^2 - 2) - 4)^2 + 2(4(5x^2 - 2)^2 - 2(5x^2 - 2) - 4) - 1) + 2| - 2) - 1) + 1 and g(x) = 1|(5(-2|(3sin(3\u03c0x + 3) - 3)| + 3)^2 + 2(-2|(3sin(3\u03c0x + 3) - 3)| + 3) + 5) - 2| + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3(2((-2((1(1x - 2))/(2(1x - 2) + 1)) - 1)/(1((1(1x - 2))/(2(1x - 2) + 1)) - 3)) + 5)^2 + 4(2((-2((1(1x - 2))/(2(1x - 2) + 1)) - 1)/(1((1(1x - 2))/(2(1x - 2) + 1)) - 3)) + 5) + 2 and g(x) = -2sin(1\u03c0((3(-3|(3x^2 - 3x) - 1| - 1) - 2)/(-1(-3|(3x^2 - 3x) - 1| - 1) + 2)) + 3) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (1((2(-1((-2(4x - 4) - 3)/(2(4x - 4) + 1)) - 4))/(-1(-1((-2(4x - 4) - 3)/(2(4x - 4) + 1)) - 4) + 2)))/(-3((2(-1((-2(4x - 4) - 3)/(2(4x - 4) + 1)) - 4))/(-1(-1((-2(4x - 4) - 3)/(2(4x - 4) + 1)) - 4) + 2)) + 2) and g(x) = (1(5((3(-3cos(2\u03c0x - 2) + 3) - 1)/(-1(-3cos(2\u03c0x - 2) + 3) - 3)) + 1) - 2)/(-3(5((3(-3cos(2\u03c0x - 2) + 3) - 1)/(-1(-3cos(2\u03c0x - 2) + 3) - 3)) + 1) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3(-2((3(-4(-3x + 5)^2 + 4(-3x + 5) + 2) - 1)/(1(-4(-3x + 5)^2 + 4(-3x + 5) + 2)))^2 + 5((3(-4(-3x + 5)^2 + 4(-3x + 5) + 2) - 1)/(1(-4(-3x + 5)^2 + 4(-3x + 5) + 2))) + 3) and g(x) = 3(3(4((2x)/(-3x + 4))^2 + 2((2x)/(-3x + 4)) + 1)^2 - 4(4((2x)/(-3x + 4))^2 + 2((2x)/(-3x + 4)) + 1) - 2) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3e^(-1(5(1(4((-3x - 2)/(1x + 1)) - 2)) - 5)) - 3 and g(x) = 5(-5(3e^(-1(-1|x - 1| - 1)) - 2) + 3) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1(-5(-1e^(1(3(-4x + 4) - 3)) + 3) + 1) + 1 and g(x) = 3((2(3e^(-1(3x - 3)) + 3) + 2)/(1(3e^(-1(3x - 3)) + 3)))^2 + 1((2(3e^(-1(3x - 3)) + 3) + 2)/(1(3e^(-1(3x - 3)) + 3))) + 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (2(2(1(-5((-3x - 1)/(1x + 1)) - 5)^2 - 5(-5((-3x - 1)/(1x + 1)) - 5) + 1)^2 - 5(1(-5((-3x - 1)/(1x + 1)) - 5)^2 - 5(-5((-3x - 1)/(1x + 1)) - 5) + 1) + 3))/(-1(2(1(-5((-3x - 1)/(1x + 1)) - 5)^2 - 5(-5((-3x - 1)/(1x + 1)) - 5) + 1)^2 - 5(1(-5((-3x - 1)/(1x + 1)) - 5)^2 - 5(-5((-3x - 1)/(1x + 1)) - 5) + 1) + 3) - 1) and g(x) = 2(4(-3e^(-2(-2x + 5)) + 2) - 3) - 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-3((-2(2(-2((3x + 1)/(-2x + 3))^2 + 1)^2 - 3(-2((3x + 1)/(-2x + 3))^2 + 1) - 5) + 3)/(2(2(-2((3x + 1)/(-2x + 3))^2 + 1)^2 - 3(-2((3x + 1)/(-2x + 3))^2 + 1) - 5) + 1)) - 3)/(-1((-2(2(-2((3x + 1)/(-2x + 3))^2 + 1)^2 - 3(-2((3x + 1)/(-2x + 3))^2 + 1) - 5) + 3)/(2(2(-2((3x + 1)/(-2x + 3))^2 + 1)^2 - 3(-2((3x + 1)/(-2x + 3))^2 + 1) - 5) + 1)) + 2) and g(x) = (1((1(-3(2|x + 2|)^2 - 3(2|x + 2|) - 5) + 1)/(3(-3(2|x + 2|)^2 - 3(2|x + 2|) - 5) - 1)) + 2)/(-3((1(-3(2|x + 2|)^2 - 3(2|x + 2|) - 5) + 1)/(3(-3(2|x + 2|)^2 - 3(2|x + 2|) - 5) - 1)) + 1) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3cos(2\u03c0((1(1|(2|(-3x^2 - 3x - 5)| - 2) + 2| + 2) + 1)/(-1(1|(2|(-3x^2 - 3x - 5)| - 2) + 2| + 2) - 3)) - 2) - 2 and g(x) = -1(1(2|((3x - 2)/(3x + 1)) + 3| - 3) + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3(-2cos(3\u03c0(2(1(-5x^2 + 5x - 3)^2 + 4(-5x^2 + 5x - 3) - 3) + 3) + 1))^2 - 2 and g(x) = (1(-3(-3|(-2e^(1x) - 1) + 3| + 2) + 1) - 1)/(3(-3(-3|(-2e^(1x) - 1) + 3| + 2) + 1) + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3|(2|((-1(1(3|x - 2| - 2) - 3) - 2)/(2(1(3|x - 2| - 2) - 3) - 1)) + 3| + 1)| + 2 and g(x) = (-1((2(-1e^(1(-3x + 4)) + 2) - 3)/(-1(-1e^(1(-3x + 4)) + 2) + 2)) - 1)/(3((2(-1e^(1(-3x + 4)) + 2) - 3)/(-1(-1e^(1(-3x + 4)) + 2) + 2)) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(5(3|(-5(-2cos(2\u03c0x - 3) + 3)^2 + 4(-2cos(2\u03c0x - 3) + 3) - 5) - 1| - 2) - 2) - 1| and g(x) = -1|(2|(1e^(-1((3x - 1)/(2x))) + 3) - 2| + 2) - 1| - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3|((1((2(1|(5x + 2) - 3|) + 1)/(-2(1|(5x + 2) - 3|) + 1)) - 2)/(1((2(1|(5x + 2) - 3|) + 1)/(-2(1|(5x + 2) - 3|) + 1)) + 1)) + 2| + 2 and g(x) = -3|(-1e^(1((-3(-1x + 5) + 2)/(2(-1x + 5) - 3))) - 2) + 1| - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3|(2|(3|((3(1cos(3\u03c0x + 1) - 1) + 3)/(2(1cos(3\u03c0x + 1) - 1) - 3)) - 3| - 3) - 1| + 1) - 1| + 1 and g(x) = (2(2cos(2\u03c0(-1|(5x^2 + 1x + 2) + 3| + 1) - 1)) - 3)/(-3(2cos(2\u03c0(-1|(5x^2 + 1x + 2) + 3| + 1) - 1)) + 4) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2|((1(-3(2(-1|x + 2| - 2)^2 - 4(-1|x + 2| - 2) + 4)^2 + 1(2(-1|x + 2| - 2)^2 - 4(-1|x + 2| - 2) + 4) + 5) - 3)/(1(-3(2(-1|x + 2| - 2)^2 - 4(-1|x + 2| - 2) + 4)^2 + 1(2(-1|x + 2| - 2)^2 - 4(-1|x + 2| - 2) + 4) + 5) - 3)) + 3| + 1 and g(x) = 3|(-3|(3(-2x + 3) + 3)| + 1)| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (3(-1|(3(5((1x)/(2x + 3)) - 5)^2 + 3(5((1x)/(2x + 3)) - 5) - 5) + 1| + 3))/(3(-1|(3(5((1x)/(2x + 3)) - 5)^2 + 3(5((1x)/(2x + 3)) - 5) - 5) + 1| + 3) - 2) and g(x) = -3|(1|(3sin(3\u03c0(-2x + 2) + 3) - 2) + 2| + 1) + 2| meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-10", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (3(2((-1(-2|(2|x - 2| - 1) + 2| - 1) + 3)/(1(-2|(2|x - 2| - 1) + 2| - 1) + 1))^2 - 3((-1(-2|(2|x - 2| - 1) + 2| - 1) + 3)/(1(-2|(2|x - 2| - 1) + 2| - 1) + 1)) + 4) - 1)/(-1(2((-1(-2|(2|x - 2| - 1) + 2| - 1) + 3)/(1(-2|(2|x - 2| - 1) + 2| - 1) + 1))^2 - 3((-1(-2|(2|x - 2| - 1) + 2| - 1) + 3)/(1(-2|(2|x - 2| - 1) + 2| - 1) + 1)) + 4) - 3) and g(x) = -1|(-4(2((-3x - 3)/(-3x + 1)) + 5)) + 3| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -4(3cos(1\u03c0(3((1((-3x - 2)/(1x - 2)) + 3)/(2((-3x - 2)/(1x - 2)) + 2)) - 4) + 2) - 3)^2 - 3(3cos(1\u03c0(3((1((-3x - 2)/(1x - 2)) + 3)/(2((-3x - 2)/(1x - 2)) + 2)) - 4) + 2) - 3) - 4 and g(x) = -3(-1((-3((-1x + 1)/(-1x)) + 1)/(-3((-1x + 1)/(-1x)) - 2))^2 - 4((-3((-1x + 1)/(-1x)) + 1)/(-3((-1x + 1)/(-1x)) - 2)) - 5)^2 + 4(-1((-3((-1x + 1)/(-1x)) + 1)/(-3((-1x + 1)/(-1x)) - 2))^2 - 4((-3((-1x + 1)/(-1x)) + 1)/(-3((-1x + 1)/(-1x)) - 2)) - 5) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the third x-coordinate (rounded to the nearest integer) where f(x) = 2|(-3|(2|(4(5x - 1)^2 + 1(5x - 1) - 5)|)| + 2) + 1| and g(x) = (2(1sin(2\u03c0(3((2x + 2)/(-1x - 1))^2 - 1) - 1) - 3) - 1)/(3(1sin(2\u03c0(3((2x + 2)/(-1x - 1))^2 - 1) - 1) - 3)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -2|(-2(-3cos(1\u03c0(-3((-2x + 1)/(-2x))^2 - 4((-2x + 1)/(-2x)) - 2) + 2)) - 3) - 3| - 3 and g(x) = -1(-2(-3|(-3|x - 2| - 3) + 1| - 1) - 1) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 5(2e^(-1(2(-4(-1x - 5) - 5) + 2)) - 1) - 5 and g(x) = -1sin(1\u03c0(-5(5(1|x + 2| - 3) + 1) + 3) + 1) + 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 2|((-1(-1|(-5(2x + 3)^2 + 3(2x + 3) + 3) + 1|) - 1)/(-3(-1|(-5(2x + 3)^2 + 3(2x + 3) + 3) + 1|) + 2))| - 2 and g(x) = (-2(-2((-2(-1x^2 - 5x + 5) + 2)/(-2(-1x^2 - 5x + 5))) + 4) - 3)/(2(-2((-2(-1x^2 - 5x + 5) + 2)/(-2(-1x^2 - 5x + 5))) + 4) - 1) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(-1(-5((2(-5x + 5) - 2)/(2(-5x + 5) + 1)))^2 - 3(-5((2(-5x + 5) - 2)/(2(-5x + 5) + 1)))) - 2)/(-3(-1(-5((2(-5x + 5) - 2)/(2(-5x + 5) + 1)))^2 - 3(-5((2(-5x + 5) - 2)/(2(-5x + 5) + 1))))) and g(x) = 5(5(3|(-2sin(1\u03c0x + 3) + 2) - 2| + 3) + 2) + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-2((-2((-2(1(1e^(1x)) - 1))/(-2(1(1e^(1x)) - 1) + 3)) + 2)/(-2((-2(1(1e^(1x)) - 1))/(-2(1(1e^(1x)) - 1) + 3)) - 3)) - 2)/(-1((-2((-2(1(1e^(1x)) - 1))/(-2(1(1e^(1x)) - 1) + 3)) + 2)/(-2((-2(1(1e^(1x)) - 1))/(-2(1(1e^(1x)) - 1) + 3)) - 3))) and g(x) = 5(1(-1|(-1sin(1\u03c0x + 2) + 2) + 3| + 2)^2 - 4(-1|(-1sin(1\u03c0x + 2) + 2) + 3| + 2) + 1)^2 - 3(1(-1|(-1sin(1\u03c0x + 2) + 2) + 3| + 2)^2 - 4(-1|(-1sin(1\u03c0x + 2) + 2) + 3| + 2) + 1) + 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1e^(-1((1(-3|(4((1x - 2)/(3x - 1)) + 1)| - 1) + 1)/(-1(-3|(4((1x - 2)/(3x - 1)) + 1)| - 1) - 3))) - 3 and g(x) = 5(3(1((-1x + 3)/(2x + 3)) - 1)^2 + 5(1((-1x + 3)/(2x + 3)) - 1) - 2) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -4(3|((2(1sin(3\u03c0(5x - 4) - 3) + 2) - 1)/(-2(1sin(3\u03c0(5x - 4) - 3) + 2) - 3)) - 3| - 2)^2 + 3(3|((2(1sin(3\u03c0(5x - 4) - 3) + 2) - 1)/(-2(1sin(3\u03c0(5x - 4) - 3) + 2) - 3)) - 3| - 2) - 3 and g(x) = -3|(1|(-1((-1x - 1)/(2x))^2 + 5((-1x - 1)/(2x)) - 4) - 2| + 3) - 3| meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2((-2(-3(2(1x + 3)^2 + 5)^2 + 1(2(1x + 3)^2 + 5) - 1))/(1(-3(2(1x + 3)^2 + 5)^2 + 1(2(1x + 3)^2 + 5) - 1) + 2))^2 + 4((-2(-3(2(1x + 3)^2 + 5)^2 + 1(2(1x + 3)^2 + 5) - 1))/(1(-3(2(1x + 3)^2 + 5)^2 + 1(2(1x + 3)^2 + 5) - 1) + 2)) + 2 and g(x) = (1((3((-3(-2|x + 3|) + 3)/(3(-2|x + 3|) + 1)) - 3)/(1((-3(-2|x + 3|) + 3)/(3(-2|x + 3|) + 1)) + 2)) + 3)/(2((3((-3(-2|x + 3|) + 3)/(3(-2|x + 3|) + 1)) - 3)/(1((-3(-2|x + 3|) + 3)/(3(-2|x + 3|) + 1)) + 2)) - 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (3(-1|((3(-2|(-2x + 4) - 3|) + 2)/(2(-2|(-2x + 4) - 3|) + 1)) - 3| + 2) + 2)/(1(-1|((3(-2|(-2x + 4) - 3|) + 2)/(2(-2|(-2x + 4) - 3|) + 1)) - 3| + 2) + 1) and g(x) = 3|(-3|(2e^(-1((-2x + 1)/(-1x))) + 2) - 3| - 2) - 3| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2|(2(2e^(-2((-3(-1|x - 1| - 1) - 2)/(-2(-1|x - 1| - 1) - 1))) - 1) + 2)| + 2 and g(x) = (2(1(1(-3x - 3)^2 + 4(-3x - 3)) - 3) - 3)/(1(1(1(-3x - 3)^2 + 4(-3x - 3)) - 3)) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2cos(1\u03c0((-3((-2((-1(1x^2 + 1x + 4) - 1)/(-2(1x^2 + 1x + 4) + 1)) + 3)/(-3((-1(1x^2 + 1x + 4) - 1)/(-2(1x^2 + 1x + 4) + 1)) + 1)) + 3)/(2((-2((-1(1x^2 + 1x + 4) - 1)/(-2(1x^2 + 1x + 4) + 1)) + 3)/(-3((-1(1x^2 + 1x + 4) - 1)/(-2(1x^2 + 1x + 4) + 1)) + 1)) - 3)) - 1) + 3 and g(x) = (-2(4(2|((-2x)/(-3x + 4)) + 2| - 3) + 3) + 1)/(-2(4(2|((-2x)/(-3x + 4)) + 2| - 3) + 3) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3(-3e^(-1(-5(4(-4x^2 - 2x)^2 - 5(-4x^2 - 2x) + 2)^2 + 1(4(-4x^2 - 2x)^2 - 5(-4x^2 - 2x) + 2) + 2)) - 1)^2 + 3 and g(x) = 4(-4(3(3|x + 3| - 3)^2 + 2(3|x + 3| - 3) + 3)^2 - 2(3(3|x + 3| - 3)^2 + 2(3|x + 3| - 3) + 3) - 3) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1|((-2(-3((-3(1sin(3\u03c0x + 2) - 1) - 1)/(2(1sin(3\u03c0x + 2) - 1) + 1)) + 2) - 1)/(3(-3((-3(1sin(3\u03c0x + 2) - 1) - 1)/(2(1sin(3\u03c0x + 2) - 1) + 1)) + 2) - 1)) - 1| + 1 and g(x) = -1(3(3(5x - 5)) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3|(1(1e^(1((-2((1x)/(-2x + 1)) - 1)/(3((1x)/(-2x + 1))))) - 3)^2 + 4(1e^(1((-2((1x)/(-2x + 1)) - 1)/(3((1x)/(-2x + 1))))) - 3) + 4)| - 1 and g(x) = -3|(-2(-1((-2x - 3)/(1x - 3))^2 - 4((-2x - 3)/(1x - 3)) + 5) - 5) + 3| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-2(-3((-3(3((2x - 3)/(1x - 3)) - 4) - 1)/(-2(3((2x - 3)/(1x - 3)) - 4) - 1))^2 - 4((-3(3((2x - 3)/(1x - 3)) - 4) - 1)/(-2(3((2x - 3)/(1x - 3)) - 4) - 1)) + 1) - 2)/(1(-3((-3(3((2x - 3)/(1x - 3)) - 4) - 1)/(-2(3((2x - 3)/(1x - 3)) - 4) - 1))^2 - 4((-3(3((2x - 3)/(1x - 3)) - 4) - 1)/(-2(3((2x - 3)/(1x - 3)) - 4) - 1)) + 1)) and g(x) = -2((2(2|((3x - 3)/(1x + 1))| - 1) - 1)/(-2(2|((3x - 3)/(1x + 1))| - 1) - 2))^2 - 1((2(2|((3x - 3)/(1x + 1))| - 1) - 1)/(-2(2|((3x - 3)/(1x + 1))| - 1) - 2)) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 4(-2|(-2|(-2sin(1\u03c0((2x - 3)/(2x - 3)) + 2) - 3) - 3| - 1) + 2| + 1) + 4 and g(x) = -1((1(-2|(3|x + 1| - 2) + 1| + 3) - 3)/(2(-2|(3|x + 1| - 2) + 1| + 3) + 1)) + 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (2(1((-3(-4((1x + 3)/(-1x + 2))^2 - 3((1x + 3)/(-1x + 2)) - 1) - 1)/(-1(-4((1x + 3)/(-1x + 2))^2 - 3((1x + 3)/(-1x + 2)) - 1) + 3))^2 + 3((-3(-4((1x + 3)/(-1x + 2))^2 - 3((1x + 3)/(-1x + 2)) - 1) - 1)/(-1(-4((1x + 3)/(-1x + 2))^2 - 3((1x + 3)/(-1x + 2)) - 1) + 3)) - 3) + 3)/(2(1((-3(-4((1x + 3)/(-1x + 2))^2 - 3((1x + 3)/(-1x + 2)) - 1) - 1)/(-1(-4((1x + 3)/(-1x + 2))^2 - 3((1x + 3)/(-1x + 2)) - 1) + 3))^2 + 3((-3(-4((1x + 3)/(-1x + 2))^2 - 3((1x + 3)/(-1x + 2)) - 1) - 1)/(-1(-4((1x + 3)/(-1x + 2))^2 - 3((1x + 3)/(-1x + 2)) - 1) + 3)) - 3) + 2) and g(x) = -1(-4(-5(-4x + 1) + 1)^2 + 5(-5(-4x + 1) + 1) + 5) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -5(2(-4(1|(3e^(-1x) + 3) + 1| + 2) - 3) - 4)^2 + 5 and g(x) = 2(-4(5(2e^(1x) + 1)^2 + 4(2e^(1x) + 1) - 1)^2 + 1) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3sin(3\u03c0((3(-5(-2|((-2x + 1)/(-1x + 3)) + 1| - 2)^2 + 2(-2|((-2x + 1)/(-1x + 3)) + 1| - 2) + 2) - 2)/(3(-5(-2|((-2x + 1)/(-1x + 3)) + 1| - 2)^2 + 2(-2|((-2x + 1)/(-1x + 3)) + 1| - 2) + 2) + 3))) - 3 and g(x) = (-2(3(5(3|x - 3| + 3) + 2)^2 - 1(5(3|x - 3| + 3) + 2) + 3) + 1)/(1(3(5(3|x - 3| + 3) + 2)^2 - 1(5(3|x - 3| + 3) + 2) + 3) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -2|(-1(1cos(1\u03c0(-1|(-2|x + 1| + 3) + 1|)) + 1)^2 + 1(1cos(1\u03c0(-1|(-2|x + 1| + 3) + 1|)) + 1) - 2) - 2| + 1 and g(x) = 1(2(-3((1x)/(-3x + 2)) - 2)) + 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 1|((-1((1((-2(2x - 4))/(-3(2x - 4) - 2)))/(3((-2(2x - 4))/(-3(2x - 4) - 2)) - 2)) - 3)/(3((1((-2(2x - 4))/(-3(2x - 4) - 2)))/(3((-2(2x - 4))/(-3(2x - 4) - 2)) - 2)) - 2)) + 1| - 1 and g(x) = -1((-1(-3((-2x)/(-3x - 1)) - 1) + 1)/(-2(-3((-2x)/(-3x - 1)) - 1) + 1))^2 - 4((-1(-3((-2x)/(-3x - 1)) - 1) + 1)/(-2(-3((-2x)/(-3x - 1)) - 1) + 1)) + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1|(-2|(-1(-2|((2x + 2)/(1x + 3)) - 1|) + 5) - 2| - 1) + 1| - 2 and g(x) = 4(-1((-3(4x + 5) + 3)/(1(4x + 5) - 3))^2 + 3((-3(4x + 5) + 3)/(1(4x + 5) - 3)) - 1) + 5 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 1((1((-1(3((1x)/(-2x - 1)) + 3) - 1)/(2(3((1x)/(-2x - 1)) + 3) + 3)) - 2)/(-2((-1(3((1x)/(-2x - 1)) + 3) - 1)/(2(3((1x)/(-2x - 1)) + 3) + 3)) - 3))^2 + 4((1((-1(3((1x)/(-2x - 1)) + 3) - 1)/(2(3((1x)/(-2x - 1)) + 3) + 3)) - 2)/(-2((-1(3((1x)/(-2x - 1)) + 3) - 1)/(2(3((1x)/(-2x - 1)) + 3) + 3)) - 3)) - 2 and g(x) = (-2(4(3cos(2\u03c0((-2x - 1)/(-2x - 2)) + 1) + 2)))/(3(4(3cos(2\u03c0((-2x - 1)/(-2x - 2)) + 1) + 2))) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -3(2|(-2|(5((-2x - 1)/(2x - 1))) + 2|) - 1| + 1) + 5 and g(x) = -3((1(5(-2sin(1\u03c0x + 1) + 1)^2 + 3(-2sin(1\u03c0x + 1) + 1) + 4) - 2)/(2(5(-2sin(1\u03c0x + 1) + 1)^2 + 3(-2sin(1\u03c0x + 1) + 1) + 4) - 1))^2 + 3((1(5(-2sin(1\u03c0x + 1) + 1)^2 + 3(-2sin(1\u03c0x + 1) + 1) + 4) - 2)/(2(5(-2sin(1\u03c0x + 1) + 1)^2 + 3(-2sin(1\u03c0x + 1) + 1) + 4) - 1)) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 5(5(-2|(1e^(2(1|x - 1| - 2)) + 1) - 1| + 2)^2 + 5(-2|(1e^(2(1|x - 1| - 2)) + 1) - 1| + 2) + 2) + 3 and g(x) = (-2(2(1|(3x + 3)|) - 3) + 1)/(-1(2(1|(3x + 3)|) - 3) + 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-1((2(5(2e^(1((-2x + 3)/(-3x))))) - 1)/(3(5(2e^(1((-2x + 3)/(-3x))))))) - 3)/(1((2(5(2e^(1((-2x + 3)/(-3x))))) - 1)/(3(5(2e^(1((-2x + 3)/(-3x)))))))) and g(x) = 1sin(1\u03c0(-3((2(-5x + 1) - 2)/(3(-5x + 1) + 2))^2 - 3((2(-5x + 1) - 2)/(3(-5x + 1) + 2))) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|(-2|((-1(-1(-1sin(1\u03c0x - 1) + 3) + 4) - 2)/(2(-1(-1sin(1\u03c0x - 1) + 3) + 4) - 1)) + 1| + 2) - 3| + 1 and g(x) = (3(2(1(-2|x + 2| - 3)^2 + 4(-2|x + 2| - 3) - 3) + 2) + 3)/(-1(2(1(-2|x + 2| - 3)^2 + 4(-2|x + 2| - 3) - 3) + 2) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3(2|(-1((-3(-2e^(-2x) - 1) + 1)/(-1(-2e^(-2x) - 1) + 3)) + 2) - 1| - 1)^2 + 1(2|(-1((-3(-2e^(-2x) - 1) + 1)/(-1(-2e^(-2x) - 1) + 3)) + 2) - 1| - 1) and g(x) = -3|(-1((-2(-3x^2 - 5x - 4) + 2)/(-3(-3x^2 - 5x - 4) - 3))^2 - 3((-2(-3x^2 - 5x - 4) + 2)/(-3(-3x^2 - 5x - 4) - 3)) - 2) - 2| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3(3(-1e^(-2((3(-3|x - 2| + 2) - 2)/(2(-3|x - 2| + 2) - 1))))^2 + 4(-1e^(-2((3(-3|x - 2| + 2) - 2)/(2(-3|x - 2| + 2) - 1)))) - 5) - 2 and g(x) = -5(1|(-4((3x - 2)/(2x + 1)) + 2)| + 2) - 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (2((-1(-5(-4(-1sin(3\u03c0x + 2))^2 + 5(-1sin(3\u03c0x + 2)) + 4)^2 + 3(-4(-1sin(3\u03c0x + 2))^2 + 5(-1sin(3\u03c0x + 2)) + 4) - 5) + 2)/(-1(-5(-4(-1sin(3\u03c0x + 2))^2 + 5(-1sin(3\u03c0x + 2)) + 4)^2 + 3(-4(-1sin(3\u03c0x + 2))^2 + 5(-1sin(3\u03c0x + 2)) + 4) - 5) - 2)) - 1)/(1((-1(-5(-4(-1sin(3\u03c0x + 2))^2 + 5(-1sin(3\u03c0x + 2)) + 4)^2 + 3(-4(-1sin(3\u03c0x + 2))^2 + 5(-1sin(3\u03c0x + 2)) + 4) - 5) + 2)/(-1(-5(-4(-1sin(3\u03c0x + 2))^2 + 5(-1sin(3\u03c0x + 2)) + 4)^2 + 3(-4(-1sin(3\u03c0x + 2))^2 + 5(-1sin(3\u03c0x + 2)) + 4) - 5) - 2))) and g(x) = 2(-2|(2((-2x - 1)/(2x + 3)) + 1) + 2| + 1) + 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (1((3((-3((3((2x)/(-1x - 1)) + 3)/(2((2x)/(-1x - 1)) - 3)) + 1)/(-1((3((2x)/(-1x - 1)) + 3)/(2((2x)/(-1x - 1)) - 3)) + 2)))/(-1((-3((3((2x)/(-1x - 1)) + 3)/(2((2x)/(-1x - 1)) - 3)) + 1)/(-1((3((2x)/(-1x - 1)) + 3)/(2((2x)/(-1x - 1)) - 3)) + 2)) + 2)) + 1)/(3((3((-3((3((2x)/(-1x - 1)) + 3)/(2((2x)/(-1x - 1)) - 3)) + 1)/(-1((3((2x)/(-1x - 1)) + 3)/(2((2x)/(-1x - 1)) - 3)) + 2)))/(-1((-3((3((2x)/(-1x - 1)) + 3)/(2((2x)/(-1x - 1)) - 3)) + 1)/(-1((3((2x)/(-1x - 1)) + 3)/(2((2x)/(-1x - 1)) - 3)) + 2)) + 2)) - 1) and g(x) = 4(-1|(-2|(2x^2 - 4x - 5) - 2|) - 3| - 3) - 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3(-1|(-5(-1|((3x)/(1x - 2)) - 3| - 3) - 3) - 2| - 1)^2 - 4(-1|(-5(-1|((3x)/(1x - 2)) - 3| - 3) - 3) - 2| - 1) - 5 and g(x) = 3|(5(2|(2x) - 3| + 3)^2 - 5(2|(2x) - 3| + 3) + 2) - 2| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1|(-4(-1(4(-2|x + 3| - 3) - 3)^2 + 5(4(-2|x + 3| - 3) - 3) - 1) + 3) + 2| - 2 and g(x) = (-3((-1(-3|(-1x + 2) + 1| + 2) + 2)/(-3(-3|(-1x + 2) + 1| + 2) - 1)) - 1)/(2((-1(-3|(-1x + 2) + 1| + 2) + 2)/(-3(-3|(-1x + 2) + 1| + 2) - 1)) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3|(1|(-1(1((-2x)/(-3x + 2))) - 2) + 1| - 1) - 2| - 2 and g(x) = 1(-2((2(-3x^2 - 2x + 2) + 3)/(2(-3x^2 - 2x + 2))) - 1) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3|(-5(2|(-1(2x + 2)^2 + 3(2x + 2) - 5)|) + 4)| - 1 and g(x) = (1(2|((-1(5x^2 + 5x) - 1)/(1(5x^2 + 5x))) + 3|) - 2)/(-1(2|((-1(5x^2 + 5x) - 1)/(1(5x^2 + 5x))) + 3|) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1(3e^(-1((-2(3(-1x + 4) + 5) - 1)/(-3(3(-1x + 4) + 5) + 4))))^2 + 3(3e^(-1((-2(3(-1x + 4) + 5) - 1)/(-3(3(-1x + 4) + 5) + 4)))) + 2 and g(x) = 3(1cos(1\u03c0(2((2x + 2)/(2x)) + 2) - 3) + 1)^2 - 4(1cos(1\u03c0(2((2x + 2)/(2x)) + 2) - 3) + 1) - 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 1(1|(4(1(-1|x + 3| - 2)^2 - 4(-1|x + 3| - 2) + 3)^2 - 5) + 3| + 2) - 1 and g(x) = 3|(5((-1(5x^2 + 3x + 1) - 3)/(-1(5x^2 + 3x + 1) + 2))) - 3| + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1|(2cos(2\u03c0(1(1(4x^2 + 2)^2 - 3) + 1) + 2) - 3) - 3| - 1 and g(x) = (-3(-1(2(4x - 5)^2 + 4(4x - 5) + 3)^2 + 5))/(-1(-1(2(4x - 5)^2 + 4(4x - 5) + 3)^2 + 5) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3(-1e^(-1((2(5((-3x + 3)/(-1x + 2)) + 4) + 2)/(-1(5((-3x + 3)/(-1x + 2)) + 4) + 2))) + 1)^2 + 4(-1e^(-1((2(5((-3x + 3)/(-1x + 2)) + 4) + 2)/(-1(5((-3x + 3)/(-1x + 2)) + 4) + 2))) + 1) - 2 and g(x) = -2((-2(-2(1sin(2\u03c0x - 1) - 2)^2 + 1(1sin(2\u03c0x - 1) - 2) + 1))/(2(-2(1sin(2\u03c0x - 1) - 2)^2 + 1(1sin(2\u03c0x - 1) - 2) + 1) - 1))^2 + 2((-2(-2(1sin(2\u03c0x - 1) - 2)^2 + 1(1sin(2\u03c0x - 1) - 2) + 1))/(2(-2(1sin(2\u03c0x - 1) - 2)^2 + 1(1sin(2\u03c0x - 1) - 2) + 1) - 1)) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -2((1(-3(-2|((-2x + 3)/(1x)) - 3|)^2 - 4(-2|((-2x + 3)/(1x)) - 3|) + 2) + 1)/(-2(-3(-2|((-2x + 3)/(1x)) - 3|)^2 - 4(-2|((-2x + 3)/(1x)) - 3|) + 2) + 1)) + 5 and g(x) = (-1((2((1(3cos(3\u03c0x + 2) + 2) - 1)/(2(3cos(3\u03c0x + 2) + 2) + 1)) - 2)/(3((1(3cos(3\u03c0x + 2) + 2) - 1)/(2(3cos(3\u03c0x + 2) + 2) + 1)) - 2)) + 2)/(-1((2((1(3cos(3\u03c0x + 2) + 2) - 1)/(2(3cos(3\u03c0x + 2) + 2) + 1)) - 2)/(3((1(3cos(3\u03c0x + 2) + 2) - 1)/(2(3cos(3\u03c0x + 2) + 2) + 1)) - 2))) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 3|(2(4(2|(1x^2 - 3x - 3) - 1| - 2)^2 - 3(2|(1x^2 - 3x - 3) - 1| - 2) - 1) - 3) - 2| + 2 and g(x) = 1e^(-1(4(-2|((1x + 2)/(-1x + 3)) + 1| + 1) - 2)) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -5(-5((2((-2(5x - 3) + 3)/(-1(5x - 3) + 2)) - 3)/(-2((-2(5x - 3) + 3)/(-1(5x - 3) + 2)) + 1)) + 4) - 4 and g(x) = (-1(3sin(1\u03c0((-2(-4x^2 + 3x - 5))/(3(-4x^2 + 3x - 5) - 2)) - 2) + 2))/(1(3sin(1\u03c0((-2(-4x^2 + 3x - 5))/(3(-4x^2 + 3x - 5) - 2)) - 2) + 2) - 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1(1(1sin(1\u03c0(5((1x + 3)/(1x + 1)) - 4) - 1) + 1)^2 - 2(1sin(1\u03c0(5((1x + 3)/(1x + 1)) - 4) - 1) + 1) + 1)^2 + 3(1(1sin(1\u03c0(5((1x + 3)/(1x + 1)) - 4) - 1) + 1)^2 - 2(1sin(1\u03c0(5((1x + 3)/(1x + 1)) - 4) - 1) + 1) + 1) + 3 and g(x) = 2e^(1(4((-3(-3|x - 1|) + 3)/(1(-3|x - 1|) - 3))^2 + 5((-3(-3|x - 1|) + 3)/(1(-3|x - 1|) - 3)) - 4)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1|(-1(-2e^(-1(-1((3x + 2)/(-3x - 1))^2 - 1((3x + 2)/(-3x - 1)) + 5)) - 2)) + 2| + 1 and g(x) = 2e^(-2(-5(3(4x^2 - 5x - 3)^2 + 4(4x^2 - 5x - 3) - 4)^2 - 1(3(4x^2 - 5x - 3)^2 + 4(4x^2 - 5x - 3) - 4) - 4)) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1((1(-1((-3(1sin(3\u03c0x + 2) - 2) + 1)/(2(1sin(3\u03c0x + 2) - 2) + 2)) - 4) - 2)/(-2(-1((-3(1sin(3\u03c0x + 2) - 2) + 1)/(2(1sin(3\u03c0x + 2) - 2) + 2)) - 4) + 3))^2 - 1((1(-1((-3(1sin(3\u03c0x + 2) - 2) + 1)/(2(1sin(3\u03c0x + 2) - 2) + 2)) - 4) - 2)/(-2(-1((-3(1sin(3\u03c0x + 2) - 2) + 1)/(2(1sin(3\u03c0x + 2) - 2) + 2)) - 4) + 3)) - 2 and g(x) = (-1((3(2(-1x - 3) + 1) - 2)/(2(2(-1x - 3) + 1) + 1)))/(2((3(2(-1x - 3) + 1) - 2)/(2(2(-1x - 3) + 1) + 1)) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2((-3(-2cos(3\u03c0(1((1x - 2)/(3x - 2)) - 2)) + 2))/(-3(-2cos(3\u03c0(1((1x - 2)/(3x - 2)) - 2)) + 2) - 2)) - 2)/(1((-3(-2cos(3\u03c0(1((1x - 2)/(3x - 2)) - 2)) + 2))/(-3(-2cos(3\u03c0(1((1x - 2)/(3x - 2)) - 2)) + 2) - 2)) + 2) and g(x) = -3e^(2(-5(-5(2x^2 + 2x - 4)) + 5)) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 4(3(-3|((1(-1x + 5) - 2)/(3(-1x + 5) + 2)) - 1| + 3) + 3) - 5 and g(x) = 5(2cos(2\u03c0((3(2|x + 1| - 3) - 2)/(-2(2|x + 1| - 3) + 3)) + 2)) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1(-3(1(1sin(3\u03c0((2x + 2)/(3x + 2))) - 3)^2 + 2(1sin(3\u03c0((2x + 2)/(3x + 2))) - 3)) - 1) - 3)/(-2(-3(1(1sin(3\u03c0((2x + 2)/(3x + 2))) - 3)^2 + 2(1sin(3\u03c0((2x + 2)/(3x + 2))) - 3)) - 1) - 2) and g(x) = (-2((1((2(-4x^2 - 2x - 3) + 3)/(-2(-4x^2 - 2x - 3) + 3)))/(-1((2(-4x^2 - 2x - 3) + 3)/(-2(-4x^2 - 2x - 3) + 3)) - 1)) + 2)/(1((1((2(-4x^2 - 2x - 3) + 3)/(-2(-4x^2 - 2x - 3) + 3)))/(-1((2(-4x^2 - 2x - 3) + 3)/(-2(-4x^2 - 2x - 3) + 3)) - 1)) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(3e^(2((-1((1(2x + 4) - 3)/(3(2x + 4) - 1)) + 3)/(-3((1(2x + 4) - 3)/(3(2x + 4) - 1)) + 2))) - 1)^2 + 4(3e^(2((-1((1(2x + 4) - 3)/(3(2x + 4) - 1)) + 3)/(-3((1(2x + 4) - 3)/(3(2x + 4) - 1)) + 2))) - 1) + 5 and g(x) = (-2((-3(-1|(-2sin(3\u03c0x - 3) - 3)| - 2) - 1)/(-2(-1|(-2sin(3\u03c0x - 3) - 3)| - 2))) + 2)/(-3((-3(-1|(-2sin(3\u03c0x - 3) - 3)| - 2) - 1)/(-2(-1|(-2sin(3\u03c0x - 3) - 3)| - 2))) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3((-1(-2|((-3((3x - 2)/(-2x + 3)) + 2)/(-3((3x - 2)/(-2x + 3)))) + 2| - 3) - 3)/(-1(-2|((-3((3x - 2)/(-2x + 3)) + 2)/(-3((3x - 2)/(-2x + 3)))) + 2| - 3)))^2 - 3((-1(-2|((-3((3x - 2)/(-2x + 3)) + 2)/(-3((3x - 2)/(-2x + 3)))) + 2| - 3) - 3)/(-1(-2|((-3((3x - 2)/(-2x + 3)) + 2)/(-3((3x - 2)/(-2x + 3)))) + 2| - 3))) + 2 and g(x) = 1(2|((2(2x - 2) + 2)/(-1(2x - 2))) + 1| - 2) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 4(2e^(-1(-4((2((3x + 3)/(1x)) - 3)/(-3((3x + 3)/(1x)) - 3)) + 1)) - 2) - 5 and g(x) = 1(4(1sin(3\u03c0(-4x + 4) + 1) + 2)^2 - 2(1sin(3\u03c0(-4x + 4) + 1) + 2) + 4) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1(-5(-4(5(3x + 3)^2 - 3(3x + 3) + 3) + 2) - 3) - 3 and g(x) = 3|(-4(5((-2x - 2)/(-1x + 3)) - 2) + 1)| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -1(-5(1|(-3e^(-2(4x^2 - 1))) - 1| - 1)^2 - 2(1|(-3e^(-2(4x^2 - 1))) - 1| - 1))^2 - 1(-5(1|(-3e^(-2(4x^2 - 1))) - 1| - 1)^2 - 2(1|(-3e^(-2(4x^2 - 1))) - 1| - 1)) + 4 and g(x) = -1|(5(-1cos(2\u03c0(-1x - 2) - 3) - 2)^2 + 1(-1cos(2\u03c0(-1x - 2) - 3) - 2) + 5) + 3| - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -4(3e^(-2((-2((-1(3x - 3) - 3)/(2(3x - 3) - 1)) + 3)/(3((-1(3x - 3) - 3)/(2(3x - 3) - 1)) - 1))) + 1) - 5 and g(x) = -1(2e^(1(-1|(4x - 4) + 2| + 3)) - 2) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2(-3((-3(-2sin(1\u03c0(-4x^2 + 4x + 3) - 3) - 2) + 2)/(2(-2sin(1\u03c0(-4x^2 + 4x + 3) - 3) - 2) - 1))^2 + 2((-3(-2sin(1\u03c0(-4x^2 + 4x + 3) - 3) - 2) + 2)/(2(-2sin(1\u03c0(-4x^2 + 4x + 3) - 3) - 2) - 1)) - 5)^2 - 1(-3((-3(-2sin(1\u03c0(-4x^2 + 4x + 3) - 3) - 2) + 2)/(2(-2sin(1\u03c0(-4x^2 + 4x + 3) - 3) - 2) - 1))^2 + 2((-3(-2sin(1\u03c0(-4x^2 + 4x + 3) - 3) - 2) + 2)/(2(-2sin(1\u03c0(-4x^2 + 4x + 3) - 3) - 2) - 1)) - 5) - 1 and g(x) = (2(1(1e^(-2(-1x - 2))) - 1) + 3)/(-3(1(1e^(-2(-1x - 2))) - 1) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 4(4(1(-1(2x + 1) - 2)^2 - 5(-1(2x + 1) - 2) - 3) - 4) - 2 and g(x) = -1cos(2\u03c0((3(-5((-3x + 1)/(1x - 3)) + 4) + 1)/(3(-5((-3x + 1)/(1x - 3)) + 4) + 3)) + 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 5((-2(-3|((-1(-3x - 2) - 2)/(-3(-3x - 2) - 1))| + 3) - 2)/(-1(-3|((-1(-3x - 2) - 2)/(-3(-3x - 2) - 1))| + 3) + 2))^2 - 3((-2(-3|((-1(-3x - 2) - 2)/(-3(-3x - 2) - 1))| + 3) - 2)/(-1(-3|((-1(-3x - 2) - 2)/(-3(-3x - 2) - 1))| + 3) + 2)) + 4 and g(x) = (-1((3(-1((-3x - 2)/(-1x - 2)) + 5) - 3)/(-1(-1((-3x - 2)/(-1x - 2)) + 5) - 1)))/(1((3(-1((-3x - 2)/(-1x - 2)) + 5) - 3)/(-1(-1((-3x - 2)/(-1x - 2)) + 5) - 1)) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -3|(1|(-2(-2|(-5x - 4) + 3| + 1) + 3) + 2| - 3)| - 2 and g(x) = (2(-2(1((3x)/(3x + 3))^2 - 4((3x)/(3x + 3)) + 3) + 5) + 2)/(1(-2(1((3x)/(3x + 3))^2 - 4((3x)/(3x + 3)) + 3) + 5)) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (2(-4(2(-1((-1x + 2)/(-2x - 3))^2 + 4((-1x + 2)/(-2x - 3)) - 3) + 4)^2 - 5(2(-1((-1x + 2)/(-2x - 3))^2 + 4((-1x + 2)/(-2x - 3)) - 3) + 4) - 3))/(1(-4(2(-1((-1x + 2)/(-2x - 3))^2 + 4((-1x + 2)/(-2x - 3)) - 3) + 4)^2 - 5(2(-1((-1x + 2)/(-2x - 3))^2 + 4((-1x + 2)/(-2x - 3)) - 3) + 4) - 3) + 3) and g(x) = (-2((1(1((1x + 1)/(3x - 2)) + 1) - 3)/(-1(1((1x + 1)/(3x - 2)) + 1))) + 3)/(2((1(1((1x + 1)/(3x - 2)) + 1) - 3)/(-1(1((1x + 1)/(3x - 2)) + 1)))) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 2|(-2(3|(5(-1x^2 + 3x + 3)^2 - 3(-1x^2 + 3x + 3)) + 3| + 1) - 2) - 2| and g(x) = 2(2((-2(-3x + 2) - 1)/(-1(-3x + 2) + 2)) + 4) + 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2|(-3|(-1((-2(-4x - 1) - 1)/(-2(-4x - 1) - 2)) - 4) + 1|) + 1| + 3 and g(x) = 3|((-2((1(3x^2 - 5x + 5) - 1)/(3(3x^2 - 5x + 5) + 1)) - 3)/(-1((1(3x^2 - 5x + 5) - 1)/(3(3x^2 - 5x + 5) + 1)) + 2)) + 1| - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(-2|((-1(-4(1e^(-2x) - 1) - 4) - 1)/(1(-4(1e^(-2x) - 1) - 4) + 3)) + 2| + 1) + 2)/(-3(-2|((-1(-4(1e^(-2x) - 1) - 4) - 1)/(1(-4(1e^(-2x) - 1) - 4) + 3)) + 2| + 1) - 1) and g(x) = (1(-3(3((2x + 1)/(-3x + 4))^2 - 2((2x + 1)/(-3x + 4)) - 4) - 1) - 2)/(2(-3(3((2x + 1)/(-3x + 4))^2 - 2((2x + 1)/(-3x + 4)) - 4) - 1) - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1(1|(3(-2e^(-2((-3x - 1)/(-1x + 2))) - 1)^2 + 3(-2e^(-2((-3x - 1)/(-1x + 2))) - 1) + 4) + 1| + 3)^2 + 3(1|(3(-2e^(-2((-3x - 1)/(-1x + 2))) - 1)^2 + 3(-2e^(-2((-3x - 1)/(-1x + 2))) - 1) + 4) + 1| + 3) - 1 and g(x) = 4(3(4(-1sin(2\u03c0x + 1) + 2)^2 + 4(-1sin(2\u03c0x + 1) + 2) - 5)^2 + 1)^2 - 3(3(4(-1sin(2\u03c0x + 1) + 2)^2 + 4(-1sin(2\u03c0x + 1) + 2) - 5)^2 + 1) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2(3((-3(2|(3|x + 1|) + 2| + 2) - 1)/(2(2|(3|x + 1|) + 2| + 2) + 3))^2 - 1((-3(2|(3|x + 1|) + 2| + 2) - 1)/(2(2|(3|x + 1|) + 2| + 2) + 3)) - 4)^2 - 4(3((-3(2|(3|x + 1|) + 2| + 2) - 1)/(2(2|(3|x + 1|) + 2| + 2) + 3))^2 - 1((-3(2|(3|x + 1|) + 2| + 2) - 1)/(2(2|(3|x + 1|) + 2| + 2) + 3)) - 4) - 1 and g(x) = -1((2(2|(-3|x - 1| + 2) - 1| - 3) + 2)/(-1(2|(-3|x - 1| + 2) - 1| - 3) - 3))^2 - 5((2(2|(-3|x - 1| + 2) - 1| - 3) + 2)/(-1(2|(-3|x - 1| + 2) - 1| - 3) - 3)) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2|(-2|(-3((-2((-1x + 3)/(1x)) - 1)/(-3((-1x + 3)/(1x)) - 1)) - 4) - 1| + 2) - 2| - 1 and g(x) = -1|(-3e^(-1(4(-1|x - 1| - 1)^2 - 5(-1|x - 1| - 1) + 2)) + 1) + 1| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -1(-1((1(-4(2x + 5) - 2) - 3)/(1(-4(2x + 5) - 2) + 1))^2 + 3((1(-4(2x + 5) - 2) - 3)/(1(-4(2x + 5) - 2) + 1))) - 3 and g(x) = 1(-3((-1(3|x - 1| - 2) - 3)/(-1(3|x - 1| - 2) - 1))^2 - 4((-1(3|x - 1| - 2) - 3)/(-1(3|x - 1| - 2) - 1)) - 3)^2 - 5(-3((-1(3|x - 1| - 2) - 3)/(-1(3|x - 1| - 2) - 1))^2 - 4((-1(3|x - 1| - 2) - 3)/(-1(3|x - 1| - 2) - 1)) - 3) + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(-1(-1((1(-3x))/(-1(-3x) + 2)) + 5) + 3) + 1 and g(x) = 2|(-3|((-2(1e^(-2x) - 2) - 1)/(-3(1e^(-2x) - 2))) + 2|)| + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-1|((1(2|(4x - 3) - 1| - 1) - 3)/(3(2|(4x - 3) - 1| - 1) - 1))|)^2 - 3(-1|((1(2|(4x - 3) - 1| - 1) - 3)/(3(2|(4x - 3) - 1| - 1) - 1))|) + 3 and g(x) = 3|(-5(3|(1|x - 3| + 2) - 1| - 3)^2 - 3(3|(1|x - 3| + 2) - 1| - 3) - 1)| - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 5(-1(1e^(2(-1((1x - 1)/(-3x))^2 + 4((1x - 1)/(-3x)) + 2)) + 2) + 2)^2 - 1(-1(1e^(2(-1((1x - 1)/(-3x))^2 + 4((1x - 1)/(-3x)) + 2)) + 2) + 2) - 5 and g(x) = -2e^(1(-2(-4((1x - 3)/(-2x - 3)) - 5))) + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -3|(4((3(-3|((-1x - 3)/(-1x)) - 2| + 3) - 1)/(3(-3|((-1x - 3)/(-1x)) - 2| + 3) + 1))^2 - 5((3(-3|((-1x - 3)/(-1x)) - 2| + 3) - 1)/(3(-3|((-1x - 3)/(-1x)) - 2| + 3) + 1)) + 3) + 1| + 3 and g(x) = (-3(2|(-2((-2x - 1)/(-2x + 3)) - 5)|) - 1)/(-1(2|(-2((-2x - 1)/(-2x + 3)) - 5)|) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2(-2e^(-1(3(-3|(-5x + 3) - 1| + 3) - 3)) + 1) - 3 and g(x) = -2((1(3|(1sin(1\u03c0x - 1) - 1) - 1| - 3))/(-2(3|(1sin(1\u03c0x - 1) - 1) - 1| - 3) + 3))^2 + 4((1(3|(1sin(1\u03c0x - 1) - 1) - 1| - 3))/(-2(3|(1sin(1\u03c0x - 1) - 1) - 1| - 3) + 3)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3(-5((-2(1(1x - 4)^2 + 2(1x - 4) - 2))/(3(1(1x - 4)^2 + 2(1x - 4) - 2)))^2 - 2) + 4 and g(x) = -1(5(5(-1x + 4) - 5))^2 - 4(5(5(-1x + 4) - 5)) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3|((-2(3(4(-4x^2 + 3x + 3) - 4) + 1) - 1)/(3(3(4(-4x^2 + 3x + 3) - 4) + 1) + 1)) + 3| - 2 and g(x) = (-3((-2((-2((2x - 2)/(-3x + 2)) - 1)/(3((2x - 2)/(-3x + 2)) - 2)) + 2)/(-3((-2((2x - 2)/(-3x + 2)) - 1)/(3((2x - 2)/(-3x + 2)) - 2)) - 1)) + 1)/(1((-2((-2((2x - 2)/(-3x + 2)) - 1)/(3((2x - 2)/(-3x + 2)) - 2)) + 2)/(-3((-2((2x - 2)/(-3x + 2)) - 1)/(3((2x - 2)/(-3x + 2)) - 2)) - 1)) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -3(1(4((-3(-4x + 2) - 3)/(2(-4x + 2) - 3)) - 4) - 5) - 3 and g(x) = 5((1(-1(-3x - 5) + 3) + 2)/(-1(-1(-3x - 5) + 3) - 2)) - 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -4((-3(1((2((1x - 3)/(-1x - 1)) - 3)/(1((1x - 3)/(-1x - 1))))^2 + 5((2((1x - 3)/(-1x - 1)) - 3)/(1((1x - 3)/(-1x - 1)))) + 3))/(2(1((2((1x - 3)/(-1x - 1)) - 3)/(1((1x - 3)/(-1x - 1))))^2 + 5((2((1x - 3)/(-1x - 1)) - 3)/(1((1x - 3)/(-1x - 1)))) + 3) + 1)) + 2 and g(x) = -2sin(2\u03c0(-1(-1(-1x - 4))^2 + 3(-1(-1x - 4)) - 4) - 3) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1(-1|((-3(4(-5x + 3)^2 - 4(-5x + 3) - 1) + 2)/(1(4(-5x + 3)^2 - 4(-5x + 3) - 1)))|)^2 - 3(-1|((-3(4(-5x + 3)^2 - 4(-5x + 3) - 1) + 2)/(1(4(-5x + 3)^2 - 4(-5x + 3) - 1)))|) - 1 and g(x) = -4(-3|(-1((3x)/(-1x + 3)) - 2)| + 2) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(-3|(3((2((-2x - 1)/(3x)) + 2)/(3((-2x - 1)/(3x)) + 3)) + 4) + 1| + 2) + 2| + 2 and g(x) = (2((-2((-3(-1x^2 - 5x - 5) + 2)/(-2(-1x^2 - 5x - 5) - 3)) + 1)/(1((-3(-1x^2 - 5x - 5) + 2)/(-2(-1x^2 - 5x - 5) - 3)) + 1)) - 1)/(-1((-2((-3(-1x^2 - 5x - 5) + 2)/(-2(-1x^2 - 5x - 5) - 3)) + 1)/(1((-3(-1x^2 - 5x - 5) + 2)/(-2(-1x^2 - 5x - 5) - 3)) + 1)) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -3(-3|((-1(1|(-2|x - 2| + 3) - 3| - 2) + 1)/(1(1|(-2|x - 2| + 3) - 3| - 2) + 2)) + 3| + 2)^2 + 4(-3|((-1(1|(-2|x - 2| + 3) - 3| - 2) + 1)/(1(1|(-2|x - 2| + 3) - 3| - 2) + 2)) + 3| + 2) + 3 and g(x) = -4(1((-2(1e^(-2x) - 1) + 2)/(-3(1e^(-2x) - 1) + 2))^2 + 3((-2(1e^(-2x) - 1) + 2)/(-3(1e^(-2x) - 1) + 2))) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1(1(-2(3(4x^2 - 4x + 5) + 3)^2 + 1(3(4x^2 - 4x + 5) + 3) - 4) - 1) + 4 and g(x) = -3(1e^(-1((1((-3x - 3)/(3x + 1)) - 1)/(1((-3x - 3)/(3x + 1)) + 2))) - 1)^2 + 5(1e^(-1((1((-3x - 3)/(3x + 1)) - 1)/(1((-3x - 3)/(3x + 1)) + 2))) - 1) + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-3(2|(-1((-3(-1e^(-1x) - 2) + 1)/(-3(-1e^(-1x) - 2) - 3))^2 - 5((-3(-1e^(-1x) - 2) + 1)/(-3(-1e^(-1x) - 2) - 3)) + 5)| - 2) + 3)/(1(2|(-1((-3(-1e^(-1x) - 2) + 1)/(-3(-1e^(-1x) - 2) - 3))^2 - 5((-3(-1e^(-1x) - 2) + 1)/(-3(-1e^(-1x) - 2) - 3)) + 5)| - 2) - 3) and g(x) = (1(1(-5(-3x^2 + 1x + 2)^2 - 1(-3x^2 + 1x + 2)) + 4))/(3(1(-5(-3x^2 + 1x + 2)^2 - 1(-3x^2 + 1x + 2)) + 4)) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -2|(-2|(1|(-2|((-1x - 2)/(-2x - 3)) + 3| + 3) + 1| + 1) - 1| + 1) + 1| and g(x) = -2(-1|(-2(-3x - 5) - 1) - 3| - 2)^2 - 4(-1|(-2(-3x - 5) - 1) - 3| - 2) - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-2(-2|(-3(2(-1|x + 3| - 3) + 2)^2 + 2(2(-1|x + 3| - 3) + 2) - 2) - 1| + 2) - 2)/(1(-2|(-3(2(-1|x + 3| - 3) + 2)^2 + 2(2(-1|x + 3| - 3) + 2) - 2) - 1| + 2) + 2) and g(x) = 1(3(-4(-4x - 2) + 3)^2 - 2(-4(-4x - 2) + 3) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3|(-4(1(-2|(1x^2 - 1x)|)^2 - 4(-2|(1x^2 - 1x)|) - 1)^2 + 3(1(-2|(1x^2 - 1x)|)^2 - 4(-2|(1x^2 - 1x)|) - 1) - 5) + 2| and g(x) = 1(-3(2|(-4x - 4) + 3| - 1)^2 - 3(2|(-4x - 4) + 3| - 1) + 2) - 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-2((-1(2(-5(-1x - 3)^2 + 1(-1x - 3) + 1)^2 - 4(-5(-1x - 3)^2 + 1(-1x - 3) + 1) - 3) + 1)/(-1(2(-5(-1x - 3)^2 + 1(-1x - 3) + 1)^2 - 4(-5(-1x - 3)^2 + 1(-1x - 3) + 1) - 3) - 1)) - 1)/(1((-1(2(-5(-1x - 3)^2 + 1(-1x - 3) + 1)^2 - 4(-5(-1x - 3)^2 + 1(-1x - 3) + 1) - 3) + 1)/(-1(2(-5(-1x - 3)^2 + 1(-1x - 3) + 1)^2 - 4(-5(-1x - 3)^2 + 1(-1x - 3) + 1) - 3) - 1)) + 3) and g(x) = 1|(1((1(2|x - 3| + 2) + 1)/(2(2|x - 3| + 2) + 2))^2 - 5((1(2|x - 3| + 2) + 1)/(2(2|x - 3| + 2) + 2)) + 4) - 2| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -4((3(2|(3|(2e^(-1x) - 1)| + 1) - 1| + 3) + 3)/(-2(2|(3|(2e^(-1x) - 1)| + 1) - 1| + 3) + 1)) + 3 and g(x) = (1(1(-1((3x)/(1x + 3)) + 3)^2 + 4(-1((3x)/(1x + 3)) + 3) - 2) - 2)/(3(1(-1((3x)/(1x + 3)) + 3)^2 + 4(-1((3x)/(1x + 3)) + 3) - 2) + 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-1(-1((1(-1((1x + 3)/(-2x + 1)) - 4) + 2)/(1(-1((1x + 3)/(-2x + 1)) - 4) + 1))^2 + 1((1(-1((1x + 3)/(-2x + 1)) - 4) + 2)/(1(-1((1x + 3)/(-2x + 1)) - 4) + 1)) + 4) + 1)/(2(-1((1(-1((1x + 3)/(-2x + 1)) - 4) + 2)/(1(-1((1x + 3)/(-2x + 1)) - 4) + 1))^2 + 1((1(-1((1x + 3)/(-2x + 1)) - 4) + 2)/(1(-1((1x + 3)/(-2x + 1)) - 4) + 1)) + 4) - 1) and g(x) = -3((-2(-1(2|x - 1|) + 5))/(1(-1(2|x - 1|) + 5) - 3)) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(-4(-2(-3|(-1|x| - 1)| + 2) - 2) + 5) - 5 and g(x) = -3|((-1((1(-5x + 1) - 2)/(2(-5x + 1) - 1)) - 3)/(-2((1(-5x + 1) - 2)/(2(-5x + 1) - 1)) + 3)) - 2| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 2(-3|(2|(-1(2|x|) + 4) - 1| + 2) - 1| + 2)^2 and g(x) = 1(1|(5(-1|x|)^2 + 1(-1|x|) - 2) + 3| - 1)^2 - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1((-2(2|((-2(-1x^2 - 2x - 1) - 3)/(1(-1x^2 - 2x - 1)))| - 3) - 3)/(-2(2|((-2(-1x^2 - 2x - 1) - 3)/(1(-1x^2 - 2x - 1)))| - 3) - 3))^2 + 5((-2(2|((-2(-1x^2 - 2x - 1) - 3)/(1(-1x^2 - 2x - 1)))| - 3) - 3)/(-2(2|((-2(-1x^2 - 2x - 1) - 3)/(1(-1x^2 - 2x - 1)))| - 3) - 3)) - 5 and g(x) = (-1(-3(3(-1e^(-2x) + 3)^2 + 3(-1e^(-2x) + 3) - 1) - 3))/(1(-3(3(-1e^(-2x) + 3)^2 + 3(-1e^(-2x) + 3) - 1) - 3) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 5(5((-1(-3(1x + 1)) + 1)/(2(-3(1x + 1)) + 2))^2 - 5((-1(-3(1x + 1)) + 1)/(2(-3(1x + 1)) + 2)) - 4) - 5 and g(x) = 2e^(2(3(-3|(2|x - 1|) + 1| - 3) + 5)) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (3((-1(-3(-3(5x - 4) - 3) + 4) + 2)/(1(-3(-3(5x - 4) - 3) + 4) - 2)) - 1)/(2((-1(-3(-3(5x - 4) - 3) + 4) + 2)/(1(-3(-3(5x - 4) - 3) + 4) - 2))) and g(x) = 3((3(-3|((3x - 1)/(-2x - 1)) - 3| + 3) - 3)/(3(-3|((3x - 1)/(-2x - 1)) - 3| + 3) - 1)) + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3|((-3(-1((-2(-2e^(-2x)) + 1)/(1(-2e^(-2x)) + 1))^2 + 5((-2(-2e^(-2x)) + 1)/(1(-2e^(-2x)) + 1)) + 5) + 1)/(-3(-1((-2(-2e^(-2x)) + 1)/(1(-2e^(-2x)) + 1))^2 + 5((-2(-2e^(-2x)) + 1)/(1(-2e^(-2x)) + 1)) + 5) + 2)) + 1| - 3 and g(x) = -3cos(1\u03c0(-1|(3|((1x + 3)/(-2x - 3)) - 2| - 1) + 3| - 1) + 2) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -4(-2|(-4(-5(2x - 2) - 5) + 1) - 1| + 1)^2 + 2(-2|(-4(-5(2x - 2) - 5) + 1) - 1| + 1) + 2 and g(x) = -4(1e^(-1(-2(-5x + 5) - 3)) - 3) - 4 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 5((3(5(-3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 4)^2 - 2(-3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 4) - 5) - 1)/(-3(5(-3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 4)^2 - 2(-3(3|x - 3| - 2)^2 - 2(3|x - 3| - 2) - 4) - 5) - 3))^2 - 4 and g(x) = -2(4(-5(1e^(-1x) - 1) - 1))^2 + 1(4(-5(1e^(-1x) - 1) - 1)) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1(-4(4((1(-1|x - 1| - 2) - 1)/(-3(-1|x - 1| - 2) + 4)) + 3)^2 + 3(4((1(-1|x - 1| - 2) - 1)/(-3(-1|x - 1| - 2) + 4)) + 3) - 4)^2 + 4(-4(4((1(-1|x - 1| - 2) - 1)/(-3(-1|x - 1| - 2) + 4)) + 3)^2 + 3(4((1(-1|x - 1| - 2) - 1)/(-3(-1|x - 1| - 2) + 4)) + 3) - 4) + 1 and g(x) = -2(2((-3((-2x - 2)/(2x)) + 2)/(-1((-2x - 2)/(2x)) + 2))^2 - 1((-3((-2x - 2)/(2x)) + 2)/(-1((-2x - 2)/(2x)) + 2)) - 2) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-3(-5((-3((-3(-2x + 5) + 1)/(2(-2x + 5) - 1)) + 2)/(1((-3(-2x + 5) + 1)/(2(-2x + 5) - 1)) + 3)) + 2) + 2)/(-2(-5((-3((-3(-2x + 5) + 1)/(2(-2x + 5) - 1)) + 2)/(1((-3(-2x + 5) + 1)/(2(-2x + 5) - 1)) + 3)) + 2) + 1) and g(x) = -1(-1((3(-1|x + 3|) - 2)/(-2(-1|x + 3|) - 2))^2 + 5((3(-1|x + 3|) - 2)/(-2(-1|x + 3|) - 2)) - 3) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1sin(3\u03c0((-1(3(-2(-4x - 1)^2 - 1(-4x - 1) - 4)^2 + 5(-2(-4x - 1)^2 - 1(-4x - 1) - 4) - 3) - 1)/(-2(3(-2(-4x - 1)^2 - 1(-4x - 1) - 4)^2 + 5(-2(-4x - 1)^2 - 1(-4x - 1) - 4) - 3) + 3)) - 3) and g(x) = (-1((1((-2(-1x - 2) + 1)/(-3(-1x - 2))) - 1)/(2((-2(-1x - 2) + 1)/(-3(-1x - 2))) + 3)) + 2)/(-2((1((-2(-1x - 2) + 1)/(-3(-1x - 2))) - 1)/(2((-2(-1x - 2) + 1)/(-3(-1x - 2))) + 3)) - 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 2e^(-1(2|(3(-3(-4x)^2 - 2(-4x))^2 + 3(-3(-4x)^2 - 2(-4x)) - 3) - 1| - 3)) - 3 and g(x) = -3|(-2e^(-2(1((3x - 3)/(-3x)) + 4)) - 1) + 2| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -2|((3(-1|(-1e^(-1(4x + 2)) - 1) + 3| + 2) + 2)/(3(-1|(-1e^(-1(4x + 2)) - 1) + 3| + 2))) - 3| + 3 and g(x) = -3|(-2(3|(-1x + 5)|) - 2) - 3| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1cos(2\u03c0(-2|(-3|(-2|(-4x - 2) - 1| - 1)|) - 3| - 3) + 1) + 1 and g(x) = -2cos(2\u03c0(1|(-4(1x^2 - 5x + 3) + 2) - 2| + 2) - 2) - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1|((-1(3(-1|((1x + 1)/(-2x)) + 1| - 3) + 5) - 3)/(-3(3(-1|((1x + 1)/(-2x)) + 1| - 3) + 5) + 2))| + 3 and g(x) = (-1(-1(5((2x - 2)/(-3x - 1)) + 5) + 1) + 1)/(2(-1(5((2x - 2)/(-3x - 1)) + 5) + 1)) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 5((3(-1((2((2x + 3)/(-1x - 1)) + 2)/(-3((2x + 3)/(-1x - 1)) - 3))^2 + 3((2((2x + 3)/(-1x - 1)) + 2)/(-3((2x + 3)/(-1x - 1)) - 3)) - 3) + 1)/(-3(-1((2((2x + 3)/(-1x - 1)) + 2)/(-3((2x + 3)/(-1x - 1)) - 3))^2 + 3((2((2x + 3)/(-1x - 1)) + 2)/(-3((2x + 3)/(-1x - 1)) - 3)) - 3) - 3))^2 + 2((3(-1((2((2x + 3)/(-1x - 1)) + 2)/(-3((2x + 3)/(-1x - 1)) - 3))^2 + 3((2((2x + 3)/(-1x - 1)) + 2)/(-3((2x + 3)/(-1x - 1)) - 3)) - 3) + 1)/(-3(-1((2((2x + 3)/(-1x - 1)) + 2)/(-3((2x + 3)/(-1x - 1)) - 3))^2 + 3((2((2x + 3)/(-1x - 1)) + 2)/(-3((2x + 3)/(-1x - 1)) - 3)) - 3) - 3)) - 1 and g(x) = -2((1(1(1x - 3) - 1) + 1)/(2(1(1x - 3) - 1))) + 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -1(2|(3(-3|(-5x^2 + 1x) + 3|) - 5) + 2| - 3)^2 - 4(2|(3(-3|(-5x^2 + 1x) + 3|) - 5) + 2| - 3) - 2 and g(x) = 2(-5(-3(1x^2 - 4x + 5)^2 + 1(1x^2 - 4x + 5) - 1)^2 - 1(-3(1x^2 - 4x + 5)^2 + 1(1x^2 - 4x + 5) - 1) - 5) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 4(-1|(-3|(-2(-2|x + 3| + 2) - 2) - 2| - 1) + 3| - 2) - 2 and g(x) = -4(-1(-3|(1|x| + 3) + 2| - 1) + 4) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2|(2((-2(-1e^(-1(-1x - 2)) - 1) + 3)/(-2(-1e^(-1(-1x - 2)) - 1) - 3))^2 - 5((-2(-1e^(-1(-1x - 2)) - 1) + 3)/(-2(-1e^(-1(-1x - 2)) - 1) - 3)) + 3) - 1| and g(x) = -4(1|((-2(-5x^2 + 3x) - 2)/(-3(-5x^2 + 3x) + 2))| - 1) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3(-2(-1(2((3x + 3)/(-2x - 3)) + 4)^2 - 2(2((3x + 3)/(-2x - 3)) + 4) - 1)^2 - 2(-1(2((3x + 3)/(-2x - 3)) + 4)^2 - 2(2((3x + 3)/(-2x - 3)) + 4) - 1) + 2)^2 - 5(-2(-1(2((3x + 3)/(-2x - 3)) + 4)^2 - 2(2((3x + 3)/(-2x - 3)) + 4) - 1)^2 - 2(-1(2((3x + 3)/(-2x - 3)) + 4)^2 - 2(2((3x + 3)/(-2x - 3)) + 4) - 1) + 2) - 1 and g(x) = -5(-1(1cos(2\u03c0((-3x + 2)/(-2x - 2)) + 1) - 2) - 3) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3(1(2|(4(-2x^2 + 4x - 2) + 1) - 1|)^2 + 2(2|(4(-2x^2 + 4x - 2) + 1) - 1|) - 4) - 3 and g(x) = -1|(-3|(2cos(1\u03c0(-2|x + 3| - 2)) - 1) - 2| + 2) - 3| + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(3cos(2\u03c0((3(-2|((-2x - 1)/(2x - 3)) - 1| - 1) + 2)/(1(-2|((-2x - 1)/(2x - 3)) - 1| - 1) - 2)) + 2) + 3)| + 1 and g(x) = 4(3cos(2\u03c0((-1((-1x)/(3x - 2)))/(3((-1x)/(3x - 2)) - 2)) - 3))^2 - 3(3cos(2\u03c0((-1((-1x)/(3x - 2)))/(3((-1x)/(3x - 2)) - 2)) - 3)) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 4(3|(3sin(1\u03c0(4(-2x)^2 + 2) - 1) + 3) + 1| + 3)^2 - 2(3|(3sin(1\u03c0(4(-2x)^2 + 2) - 1) + 3) + 1| + 3) + 2 and g(x) = 1|(-5((-1(-4x^2 - 5x + 3) + 2)/(-1(-4x^2 - 5x + 3))) - 1) - 1| - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4((-2(3((1((2x - 2)/(3x)) + 1)/(3((2x - 2)/(3x)))) + 1) + 1)/(2(3((1((2x - 2)/(3x)) + 1)/(3((2x - 2)/(3x)))) + 1)))^2 - 2((-2(3((1((2x - 2)/(3x)) + 1)/(3((2x - 2)/(3x)))) + 1) + 1)/(2(3((1((2x - 2)/(3x)) + 1)/(3((2x - 2)/(3x)))) + 1))) - 3 and g(x) = 1(-2e^(1(2(2|x|) - 3)) + 2) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3((3(3(2e^(1((-1x - 3)/(-3x - 1))) - 3) - 4))/(-1(3(2e^(1((-1x - 3)/(-3x - 1))) - 3) - 4) - 1)) + 1)/(3((3(3(2e^(1((-1x - 3)/(-3x - 1))) - 3) - 4))/(-1(3(2e^(1((-1x - 3)/(-3x - 1))) - 3) - 4) - 1)) - 2) and g(x) = 4(-2((2((-1x + 1)/(-1x - 2)) + 3)/(3((-1x + 1)/(-1x - 2)) + 3)) + 2)^2 - 3(-2((2((-1x + 1)/(-1x - 2)) + 3)/(3((-1x + 1)/(-1x - 2)) + 3)) + 2) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -3(2((-1(2|((1x - 2)/(1x - 2)) + 3| - 1) + 2)/(2(2|((1x - 2)/(1x - 2)) + 3| - 1) - 1)) + 3)^2 + 4(2((-1(2|((1x - 2)/(1x - 2)) + 3| - 1) + 2)/(2(2|((1x - 2)/(1x - 2)) + 3| - 1) - 1)) + 3) - 4 and g(x) = -3(-1((1((2x - 3)/(-1x)) + 3)/(3((2x - 3)/(-1x)) - 1))^2 + 2((1((2x - 3)/(-1x)) + 3)/(3((2x - 3)/(-1x)) - 1)) - 1)^2 + 4(-1((1((2x - 3)/(-1x)) + 3)/(3((2x - 3)/(-1x)) - 1))^2 + 2((1((2x - 3)/(-1x)) + 3)/(3((2x - 3)/(-1x)) - 1)) - 1) - 5 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3(1(-1(-2((-3x + 1)/(-3x + 2)) + 5)^2 + 2(-2((-3x + 1)/(-3x + 2)) + 5)) - 2)^2 + 3(1(-1(-2((-3x + 1)/(-3x + 2)) + 5)^2 + 2(-2((-3x + 1)/(-3x + 2)) + 5)) - 2) and g(x) = (2(5(-2(3|x - 2| + 1)^2) + 1) - 1)/(2(5(-2(3|x - 2| + 1)^2) + 1) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -4((2(-4((-1(-3|x| + 3) - 1)/(-1(-3|x| + 3) - 1)) - 4) - 2)/(3(-4((-1(-3|x| + 3) - 1)/(-1(-3|x| + 3) - 1)) - 4) - 1)) + 2 and g(x) = 1|(-2e^(-2(-3((-1x - 3)/(2x - 1))^2 + 2((-1x - 3)/(2x - 1)) + 3)) - 3) + 2| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(-3|(-2((-1((3x + 2)/(2x)) - 2)/(1((3x + 2)/(2x)) - 3))^2 - 3((-1((3x + 2)/(2x)) - 2)/(1((3x + 2)/(2x)) - 3)) + 1) + 1| - 1) - 3)/(1(-3|(-2((-1((3x + 2)/(2x)) - 2)/(1((3x + 2)/(2x)) - 3))^2 - 3((-1((3x + 2)/(2x)) - 2)/(1((3x + 2)/(2x)) - 3)) + 1) + 1| - 1) - 2) and g(x) = 3((-3(-4(-1x)^2 - 3(-1x) + 4) + 2)/(1(-4(-1x)^2 - 3(-1x) + 4))) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1((-3(4((1(1|x - 2| + 1) + 3)/(2(1|x - 2| + 1) - 1)) - 3) + 2)/(-1(4((1(1|x - 2| + 1) + 3)/(2(1|x - 2| + 1) - 1)) - 3))) + 2 and g(x) = 1(-3e^(-1(1(1|x - 2| - 2)^2 + 4(1|x - 2| - 2) + 5)) + 2)^2 - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -2(-1|(2|((-1(-5x + 5) + 1)/(-2(-5x + 5))) + 2| - 3) + 1| - 3)^2 + 4(-1|(2|((-1(-5x + 5) + 1)/(-2(-5x + 5))) + 2| - 3) + 1| - 3) + 5 and g(x) = (1(1(2(-1|x + 3| + 1)^2 - 1(-1|x + 3| + 1) - 5) - 1) - 2)/(2(1(2(-1|x + 3| + 1)^2 - 1(-1|x + 3| + 1) - 5) - 1) - 1) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -3(-5((-2(1(1sin(3\u03c0x + 1) - 1) + 1) - 3)/(2(1(1sin(3\u03c0x + 1) - 1) + 1) + 2))^2 + 5((-2(1(1sin(3\u03c0x + 1) - 1) + 1) - 3)/(2(1(1sin(3\u03c0x + 1) - 1) + 1) + 2))) - 5 and g(x) = 2|(-1|((-3(4x + 1) - 2)/(1(4x + 1) + 3)) - 2| + 2) + 1| - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3e^(-1(-3(-5(2(-2x - 1) + 2)^2 - 1(2(-2x - 1) + 2) + 2)^2 + 5(-5(2(-2x - 1) + 2)^2 - 1(2(-2x - 1) + 2) + 2) + 4)) - 2 and g(x) = -3(2|(1e^(-2(-1|x - 1| + 1)) + 1) + 2| - 2)^2 + 5(2|(1e^(-2(-1|x - 1| + 1)) + 1) + 2| - 2) - 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1(2|(-3(5(-3x + 2)^2 - 2(-3x + 2) - 4))| - 3) + 1 and g(x) = -5(5(3|(-3x^2 + 5x + 1)| + 2) + 5) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -1e^(-1(-4((1(4(-3|x - 1| + 1) + 3) - 2)/(1(4(-3|x - 1| + 1) + 3)))^2 + 2)) + 2 and g(x) = (1(5(1|(5x - 4) + 1|) - 3) + 1)/(2(5(1|(5x - 4) + 1|) - 3) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1(3|(-5(5((2x - 2)/(1x - 2))^2 - 2((2x - 2)/(1x - 2)) - 4) + 4) + 3| + 2)^2 + 4(3|(-5(5((2x - 2)/(1x - 2))^2 - 2((2x - 2)/(1x - 2)) - 4) + 4) + 3| + 2) - 3 and g(x) = 4(-4((1((2x + 2)/(1x - 3)) - 2)/(2((2x + 2)/(1x - 3)) + 2)) + 3) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -2(1|(-2((1((-3x - 1)/(2x - 1)) + 1)/(-1((-3x - 1)/(2x - 1)) - 1)) - 3) + 1| + 2) and g(x) = -1((-2((-1(-1|x - 2| + 3) - 3)/(-1(-1|x - 2| + 3) + 2)) + 2)/(-1((-1(-1|x - 2| + 3) - 3)/(-1(-1|x - 2| + 3) + 2)) + 3))^2 - 4((-2((-1(-1|x - 2| + 3) - 3)/(-1(-1|x - 2| + 3) + 2)) + 2)/(-1((-1(-1|x - 2| + 3) - 3)/(-1(-1|x - 2| + 3) + 2)) + 3)) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-8", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 3|(2(2|(1(2|x + 2| - 2) + 1) + 1| + 3)^2 - 3(2|(1(2|x + 2| - 2) + 1) + 1| + 3) + 1) - 2| - 2 and g(x) = 1(1(-1|(3|x + 1| + 1) - 1| + 3)^2 - 3(-1|(3|x + 1| + 1) - 1| + 3) + 5)^2 + 5(1(-1|(3|x + 1| + 1) - 1| + 3)^2 - 3(-1|(3|x + 1| + 1) - 1| + 3) + 5) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (1(5((2((-2(2x^2 - 3x + 4) + 2)/(1(2x^2 - 3x + 4) + 2)) + 3)/(3((-2(2x^2 - 3x + 4) + 2)/(1(2x^2 - 3x + 4) + 2)) - 2))^2 + 5((2((-2(2x^2 - 3x + 4) + 2)/(1(2x^2 - 3x + 4) + 2)) + 3)/(3((-2(2x^2 - 3x + 4) + 2)/(1(2x^2 - 3x + 4) + 2)) - 2))))/(-1(5((2((-2(2x^2 - 3x + 4) + 2)/(1(2x^2 - 3x + 4) + 2)) + 3)/(3((-2(2x^2 - 3x + 4) + 2)/(1(2x^2 - 3x + 4) + 2)) - 2))^2 + 5((2((-2(2x^2 - 3x + 4) + 2)/(1(2x^2 - 3x + 4) + 2)) + 3)/(3((-2(2x^2 - 3x + 4) + 2)/(1(2x^2 - 3x + 4) + 2)) - 2))) - 1) and g(x) = (2(-1|(1(2sin(2\u03c0x - 3) - 1) - 2) - 3| + 3) - 2)/(3(-1|(1(2sin(2\u03c0x - 3) - 1) - 2) - 3| + 3) - 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3|(-1(-3(-2|(-3|x - 2|) - 2| - 1) + 4) + 1) + 1| + 3 and g(x) = 2e^(-1((-2(-2|(3|x + 2| + 1) - 1|) - 3)/(3(-2|(3|x + 2| + 1) - 1|) + 1))) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1e^(1((-1(-3((2((-2x + 2)/(1x - 2)) - 2)/(-2((-2x + 2)/(1x - 2)) + 3)) + 4) + 2)/(-3(-3((2((-2x + 2)/(1x - 2)) - 2)/(-2((-2x + 2)/(1x - 2)) + 3)) + 4) + 1))) + 3 and g(x) = 1e^(-2(2|(3|((-3x + 1)/(3x + 3)) + 3| - 1)| + 2)) - 1 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (1(-3(-2|(-3|(3x^2 + 3x + 1) + 3| + 3)| - 2) - 2) + 3)/(3(-3(-2|(-3|(3x^2 + 3x + 1) + 3| + 3)| - 2) - 2) + 3) and g(x) = (2(3((2((-2x + 2)/(3x - 2)) + 2)/(1((-2x + 2)/(3x - 2)) + 2))^2 - 4((2((-2x + 2)/(3x - 2)) + 2)/(1((-2x + 2)/(3x - 2)) + 2)) - 4) + 3)/(-1(3((2((-2x + 2)/(3x - 2)) + 2)/(1((-2x + 2)/(3x - 2)) + 2))^2 - 4((2((-2x + 2)/(3x - 2)) + 2)/(1((-2x + 2)/(3x - 2)) + 2)) - 4) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3(2((3(4(-4x^2 + 5x - 1)^2 - 5(-4x^2 + 5x - 1) + 1) - 3)/(-1(4(-4x^2 + 5x - 1)^2 - 5(-4x^2 + 5x - 1) + 1)))^2 + 4((3(4(-4x^2 + 5x - 1)^2 - 5(-4x^2 + 5x - 1) + 1) - 3)/(-1(4(-4x^2 + 5x - 1)^2 - 5(-4x^2 + 5x - 1) + 1))) - 2)^2 - 2(2((3(4(-4x^2 + 5x - 1)^2 - 5(-4x^2 + 5x - 1) + 1) - 3)/(-1(4(-4x^2 + 5x - 1)^2 - 5(-4x^2 + 5x - 1) + 1)))^2 + 4((3(4(-4x^2 + 5x - 1)^2 - 5(-4x^2 + 5x - 1) + 1) - 3)/(-1(4(-4x^2 + 5x - 1)^2 - 5(-4x^2 + 5x - 1) + 1))) - 2) + 1 and g(x) = -4(5(-1(-2|x - 2| - 3) + 5)) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -2(1(1|((1(-2x - 2) + 2)/(2(-2x - 2) + 2)) + 3| + 3) - 5) + 2 and g(x) = -2e^(-1(-2(2((-1x + 2)/(-3x - 3))^2 - 2((-1x + 2)/(-3x - 3)))^2 + 2(2((-1x + 2)/(-3x - 3))^2 - 2((-1x + 2)/(-3x - 3))) + 2)) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2(-5(-3|(-5(4x) - 1) - 1| - 3)^2 + 5(-3|(-5(4x) - 1) - 1| - 3) + 5) and g(x) = -2(2((3(-5x + 4) + 1)/(2(-5x + 4) - 1)) + 3)^2 - 3(2((3(-5x + 4) + 1)/(2(-5x + 4) - 1)) + 3) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-1(2(1cos(2\u03c0(-1(-2x^2 - 4)) - 2) - 1)^2 + 2) - 3)/(1(2(1cos(2\u03c0(-1(-2x^2 - 4)) - 2) - 1)^2 + 2) + 3) and g(x) = -1(-1|(5(-3x + 2) + 2) - 2|) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -4((-3(-1(-2(-2x + 1)^2 - 3(-2x + 1) + 5) - 3) - 2)/(2(-1(-2(-2x + 1)^2 - 3(-2x + 1) + 5) - 3)))^2 - 1((-3(-1(-2(-2x + 1)^2 - 3(-2x + 1) + 5) - 3) - 2)/(2(-1(-2(-2x + 1)^2 - 3(-2x + 1) + 5) - 3))) + 3 and g(x) = 2sin(1\u03c0((-1((-1(2|x + 1|) + 3)/(1(2|x + 1|) + 2)) + 3)/(2((-1(2|x + 1|) + 3)/(1(2|x + 1|) + 2)))) + 1) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 5(-3(-2(1(-2|x| + 3)^2 - 4(-2|x| + 3) + 4) + 5) + 3) - 1 and g(x) = -2(1((-1(2x + 3) + 2)/(3(2x + 3) + 1)) + 3)^2 - 4(1((-1(2x + 3) + 2)/(3(2x + 3) + 1)) + 3) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1sin(3\u03c0((-1(4(-5(-4x^2 - 2x + 5) + 4)^2 + 5(-5(-4x^2 - 2x + 5) + 4) + 1) - 2)/(1(4(-5(-4x^2 - 2x + 5) + 4)^2 + 5(-5(-4x^2 - 2x + 5) + 4) + 1) - 3)) - 1) + 3 and g(x) = -3((2(-1(1x - 2) + 2) + 3)/(2(-1(1x - 2) + 2) - 1)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -2e^(-2((-2(-2|((2((-2x + 1)/(2x + 3)))/(-1((-2x + 1)/(2x + 3)) + 2)) - 2| + 2) - 1)/(-1(-2|((2((-2x + 1)/(2x + 3)))/(-1((-2x + 1)/(2x + 3)) + 2)) - 2| + 2) + 2))) - 1 and g(x) = -3|(-2|(-1(-3e^(1x) + 1) - 1) + 1| - 3) - 1| in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1|(-3(1(-5(1x^2 - 5) - 4)^2 + 3(-5(1x^2 - 5) - 4) + 4) + 5) - 1| and g(x) = 5(4(-2((-1x - 1)/(1x + 1))^2 + 5((-1x - 1)/(1x + 1)) - 1) + 4)^2 + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2|(5(2(-2|(-1e^(-2x) + 1) - 1|)^2)) - 3| and g(x) = (-1(4(4((1x - 3)/(1x - 3)))^2 - 1(4((1x - 3)/(1x - 3))) + 5) - 1)/(-1(4(4((1x - 3)/(1x - 3)))^2 - 1(4((1x - 3)/(1x - 3))) + 5) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -3(5(2(1e^(1(2x - 4)) + 2)^2 - 5(1e^(1(2x - 4)) + 2) + 2)^2 - 3(2(1e^(1(2x - 4)) + 2)^2 - 5(1e^(1(2x - 4)) + 2) + 2) + 2)^2 + 4(5(2(1e^(1(2x - 4)) + 2)^2 - 5(1e^(1(2x - 4)) + 2) + 2)^2 - 3(2(1e^(1(2x - 4)) + 2)^2 - 5(1e^(1(2x - 4)) + 2) + 2) + 2) + 2 and g(x) = (2(1(-4((-2x + 2)/(-3x)) - 5) - 5))/(-1(1(-4((-2x + 2)/(-3x)) - 5) - 5) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 2e^(2((2(-1((-2((1x + 3)/(2x + 1)) - 1)/(2((1x + 3)/(2x + 1)) + 2)) + 2) + 3)/(-2(-1((-2((1x + 3)/(2x + 1)) - 1)/(2((1x + 3)/(2x + 1)) + 2)) + 2) + 1))) + 1 and g(x) = -3(-5(1sin(2\u03c0(1x^2 - 1x - 2) - 3) + 3) - 2) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3((2(1|(-3|((-2x + 2)/(1x)) - 2| + 1) + 2| + 3) - 1)/(-1(1|(-3|((-2x + 2)/(1x)) - 2| + 1) + 2| + 3) - 2)) - 1)/(3((2(1|(-3|((-2x + 2)/(1x)) - 2| + 1) + 2| + 3) - 1)/(-1(1|(-3|((-2x + 2)/(1x)) - 2| + 1) + 2| + 3) - 2)) - 2) and g(x) = -1((1((2((-1x + 1)/(-3x - 3)))/(-3((-1x + 1)/(-3x - 3)) - 3)) + 2)/(-1((2((-1x + 1)/(-3x - 3)))/(-3((-1x + 1)/(-3x - 3)) - 3)) + 2))^2 - 4((1((2((-1x + 1)/(-3x - 3)))/(-3((-1x + 1)/(-3x - 3)) - 3)) + 2)/(-1((2((-1x + 1)/(-3x - 3)))/(-3((-1x + 1)/(-3x - 3)) - 3)) + 2)) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 2e^(-2(2((2(-5((-1x - 2)/(1x - 3))^2 - 1((-1x - 2)/(1x - 3)) + 1) - 3)/(1(-5((-1x - 2)/(1x - 3))^2 - 1((-1x - 2)/(1x - 3)) + 1) + 2))^2 - 4((2(-5((-1x - 2)/(1x - 3))^2 - 1((-1x - 2)/(1x - 3)) + 1) - 3)/(1(-5((-1x - 2)/(1x - 3))^2 - 1((-1x - 2)/(1x - 3)) + 1) + 2)) + 4)) and g(x) = (3(-3((2(-2x + 4) - 3)/(3(-2x + 4) - 2)) - 1) + 2)/(2(-3((2(-2x + 4) - 3)/(3(-2x + 4) - 2)) - 1) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (2(-1|(3(4(3|x - 3|)^2 + 4(3|x - 3|) - 1)^2 + 4(4(3|x - 3|)^2 + 4(3|x - 3|) - 1) + 4) + 1| - 1) - 1)/(1(-1|(3(4(3|x - 3|)^2 + 4(3|x - 3|) - 1)^2 + 4(4(3|x - 3|)^2 + 4(3|x - 3|) - 1) + 4) + 1| - 1) + 3) and g(x) = -1(-4((-3(-2|x - 3| + 3) - 1)/(-3(-2|x - 3| + 3) + 2)) - 3) + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2|(-5(-1(2e^(-1(-1x + 3)) - 1) + 2)^2 + 1(-1(2e^(-1(-1x + 3)) - 1) + 2) - 3) + 1| + 2 and g(x) = 3|(5(4(-2e^(-1x) - 2) - 5)^2 - 3(4(-2e^(-1x) - 2) - 5) + 4)| - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (1(-5(-3(2(2x^2 - 2x + 5)^2 + 4(2x^2 - 2x + 5)) + 2) + 2) - 1)/(-3(-5(-3(2(2x^2 - 2x + 5)^2 + 4(2x^2 - 2x + 5)) + 2) + 2) - 1) and g(x) = 1(-1e^(2((1(5x - 2) - 3)/(2(5x - 2) - 1))) - 1) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (2(-1|((1(1(1sin(2\u03c0x - 1) - 1)^2 - 4(1sin(2\u03c0x - 1) - 1) + 5) - 3)/(-2(1(1sin(2\u03c0x - 1) - 1)^2 - 4(1sin(2\u03c0x - 1) - 1) + 5) - 2)) + 1| + 2) - 1)/(1(-1|((1(1(1sin(2\u03c0x - 1) - 1)^2 - 4(1sin(2\u03c0x - 1) - 1) + 5) - 3)/(-2(1(1sin(2\u03c0x - 1) - 1)^2 - 4(1sin(2\u03c0x - 1) - 1) + 5) - 2)) + 1| + 2) + 2) and g(x) = 1|(2(-3((-3x - 2)/(-1x))^2 - 4((-3x - 2)/(-1x)) - 2)^2 + 4(-3((-3x - 2)/(-1x))^2 - 4((-3x - 2)/(-1x)) - 2) + 1) + 2| - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-2(-3(4((2(-4x^2 - 2x - 1) + 1)/(1(-4x^2 - 2x - 1))) + 3)^2 + 2(4((2(-4x^2 - 2x - 1) + 1)/(1(-4x^2 - 2x - 1))) + 3) + 5) - 2)/(-2(-3(4((2(-4x^2 - 2x - 1) + 1)/(1(-4x^2 - 2x - 1))) + 3)^2 + 2(4((2(-4x^2 - 2x - 1) + 1)/(1(-4x^2 - 2x - 1))) + 3) + 5)) and g(x) = -1(-3(3(-3x + 1)^2 + 3(-3x + 1) + 1)^2 - 4(3(-3x + 1)^2 + 3(-3x + 1) + 1) + 4) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 4(1cos(3\u03c0((2(1((-1x + 2)/(-1x + 2)) + 4))/(-1(1((-1x + 2)/(-1x + 2)) + 4) - 1)) + 1) + 3) + 4 and g(x) = (2((-2(-1(1x - 2) + 3))/(3(-1(1x - 2) + 3) + 1)) - 1)/(-2((-2(-1(1x - 2) + 3))/(3(-1(1x - 2) + 3) + 1)) - 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3e^(2(-1((1(-1(3|x + 2| + 3) - 5) + 3)/(-2(-1(3|x + 2| + 3) - 5) + 3))^2 + 1((1(-1(3|x + 2| + 3) - 5) + 3)/(-2(-1(3|x + 2| + 3) - 5) + 3)) - 1)) + 2 and g(x) = (-2((1(2(-2e^(1x) - 2) + 4))/(3(2(-2e^(1x) - 2) + 4) + 3)) + 1)/(1((1(2(-2e^(1x) - 2) + 4))/(3(2(-2e^(1x) - 2) + 4) + 3)) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -1|(-2|(-3((1(2|x - 1| - 1) + 2)/(-3(2|x - 1| - 1) - 2)) + 3) + 3| + 2) - 3| - 2 and g(x) = -1(5(1(-5x^2 + 3x - 1)^2 + 3(-5x^2 + 3x - 1) - 1) - 3) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1|((2(3((-3(1|x - 3| - 1) - 1)/(2(1|x - 3| - 1) + 1)) + 1) - 1)/(3(3((-3(1|x - 3| - 1) - 1)/(2(1|x - 3| - 1) + 1)) + 1) + 2)) - 3| - 3 and g(x) = -4((2(-3((2x - 2)/(-3x - 2)) + 3) - 1)/(-3(-3((2x - 2)/(-3x - 2)) + 3)))^2 + 1((2(-3((2x - 2)/(-3x - 2)) + 3) - 1)/(-3(-3((2x - 2)/(-3x - 2)) + 3))) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-3((-2(-5(3(1x) + 1)^2 + 3(3(1x) + 1) + 3) - 2)/(-2(-5(3(1x) + 1)^2 + 3(3(1x) + 1) + 3) - 1)))/(-2((-2(-5(3(1x) + 1)^2 + 3(3(1x) + 1) + 3) - 2)/(-2(-5(3(1x) + 1)^2 + 3(3(1x) + 1) + 3) - 1)) + 1) and g(x) = 2(1(1cos(3\u03c0(-1|x| - 1) + 3) - 3)^2 - 4(1cos(3\u03c0(-1|x| - 1) + 3) - 3) + 4) - 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3|(1|(1(1|(-2|x - 1| - 3) - 1|)^2 + 4(1|(-2|x - 1| - 3) - 1|) - 4) - 1|) + 3| and g(x) = 2|((-2(5((-3x - 2)/(-1x + 3))^2 + 5((-3x - 2)/(-1x + 3)) - 3) + 2)/(-3(5((-3x - 2)/(-1x + 3))^2 + 5((-3x - 2)/(-1x + 3)) - 3) - 2)) - 1| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (1(2(5(-1|(4x^2 + 2x - 3) + 3|) - 3)^2 - 3(5(-1|(4x^2 + 2x - 3) + 3|) - 3) - 5) + 2)/(-1(2(5(-1|(4x^2 + 2x - 3) + 3|) - 3)^2 - 3(5(-1|(4x^2 + 2x - 3) + 3|) - 3) - 5) + 3) and g(x) = -2|((-2(-2(-2e^(2x)) + 1) + 2)/(-3(-2(-2e^(2x)) + 1) - 2)) + 2| + 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-7", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 3|((-3((1(1|(-5x + 1) - 3| + 2) + 2)/(-3(1|(-5x + 1) - 3| + 2) - 3)) + 2)/(-1((1(1|(-5x + 1) - 3| + 2) + 2)/(-3(1|(-5x + 1) - 3| + 2) - 3)) + 2)) + 2| - 3 and g(x) = 2|((1(-3(-4x + 1) + 4) + 1)/(-1(-3(-4x + 1) + 4) + 2)) + 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(-1|(-3(3|((-3x - 2)/(2x - 3)) + 2|)^2 + 2(3|((-3x - 2)/(2x - 3)) + 2|) + 1) - 1|) - 2 and g(x) = -2e^(1(2|(-5((-2x + 1)/(2x - 1))^2 + 3)|)) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -4(-1|(2|((-2(5x + 3) - 3)/(-3(5x + 3) + 1)) + 2| - 2) + 2| - 2) + 2 and g(x) = 1(2(2((-2x - 1)/(1x - 2)) + 1) + 5) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -1|((-2(1(-4(-3|x| + 2)^2 - 1(-3|x| + 2) - 2)^2 - 3(-4(-3|x| + 2)^2 - 1(-3|x| + 2) - 2) + 3) - 1)/(3(1(-4(-3|x| + 2)^2 - 1(-3|x| + 2) - 2)^2 - 3(-4(-3|x| + 2)^2 - 1(-3|x| + 2) - 2) + 3) - 2)) - 3| - 1 and g(x) = -4(5(-4(-2e^(-2x) + 2)^2 - 1(-2e^(-2x) + 2) + 5)) + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -4(-4(-1(4(1sin(2\u03c0x - 3) + 3) - 3) - 2)^2 - 1(-1(4(1sin(2\u03c0x - 3) + 3) - 3) - 2) + 3)^2 + 3(-4(-1(4(1sin(2\u03c0x - 3) + 3) - 3) - 2)^2 - 1(-1(4(1sin(2\u03c0x - 3) + 3) - 3) - 2) + 3) + 1 and g(x) = -3(-4(-4((2x)/(-2x - 1))^2 - 5((2x)/(-2x - 1)) - 1) - 3)^2 + 2(-4(-4((2x)/(-2x - 1))^2 - 5((2x)/(-2x - 1)) - 1) - 3) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -4(1e^(1(-3|(-4(3|x - 2|)^2 + 5(3|x - 2|) - 5) - 3| - 1)) + 1)^2 + 4(1e^(1(-3|(-4(3|x - 2|)^2 + 5(3|x - 2|) - 5) - 3| - 1)) + 1) + 3 and g(x) = 4((1(-1((-1x - 3)/(2x + 2)) - 5) + 3)/(-2(-1((-1x - 3)/(2x + 2)) - 5) + 3)) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (2((-1(3|((-1(3x - 1) - 1)/(-2(3x - 1) + 3)) - 2| - 1) + 1)/(2(3|((-1(3x - 1) - 1)/(-2(3x - 1) + 3)) - 2| - 1) + 1)) + 2)/(-2((-1(3|((-1(3x - 1) - 1)/(-2(3x - 1) + 3)) - 2| - 1) + 1)/(2(3|((-1(3x - 1) - 1)/(-2(3x - 1) + 3)) - 2| - 1) + 1)) + 3) and g(x) = -1|((-3(-1|(-1|x + 3| - 3) + 1|))/(1(-1|(-1|x + 3| - 3) + 1|) + 1)) - 2| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -5((-2(-1e^(-1(-1(1x + 3)^2 + 1(1x + 3) + 4)) + 2) - 3)/(1(-1e^(-1(-1(1x + 3)^2 + 1(1x + 3) + 4)) + 2) + 2)) - 3 and g(x) = -4(-3((2(1x - 3) - 1)/(-2(1x - 3) + 3)) + 2)^2 + 4(-3((2(1x - 3) - 1)/(-2(1x - 3) + 3)) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1(2|(3(1|((-3x - 3)/(2x - 3)) + 1| - 2)^2 - 4(1|((-3x - 3)/(2x - 3)) + 1| - 2) + 4) - 3| - 1) + 5 and g(x) = 3|(3|((-2((2x - 3)/(3x + 2)) - 1)/(2((2x - 3)/(3x + 2)) - 1)) - 2|) + 3| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 2|(1|(3|((3(1x + 2) + 1)/(-2(1x + 2) + 3)) + 1| + 3) + 3| + 1) - 1| - 1 and g(x) = 1|(-2e^(-2(-2|(-3x - 3) + 1|)) + 1) - 2| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (2((-3(-3(-1(-1x - 1)^2 - 5(-1x - 1) + 4)^2 - 2(-1(-1x - 1)^2 - 5(-1x - 1) + 4) - 5) + 3)/(-2(-3(-1(-1x - 1)^2 - 5(-1x - 1) + 4)^2 - 2(-1(-1x - 1)^2 - 5(-1x - 1) + 4) - 5) - 2)) + 2)/(2((-3(-3(-1(-1x - 1)^2 - 5(-1x - 1) + 4)^2 - 2(-1(-1x - 1)^2 - 5(-1x - 1) + 4) - 5) + 3)/(-2(-3(-1(-1x - 1)^2 - 5(-1x - 1) + 4)^2 - 2(-1(-1x - 1)^2 - 5(-1x - 1) + 4) - 5) - 2))) and g(x) = -3|(2e^(1(-1|(-2|x + 1| - 2) + 1| + 3)))| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-2(3cos(2\u03c0(2|(4(1x + 5)^2 + 4(1x + 5) - 2)| - 3) + 2) + 3) - 2)/(2(3cos(2\u03c0(2|(4(1x + 5)^2 + 4(1x + 5) - 2)| - 3) + 2) + 3) + 2) and g(x) = 2((-3(-2|(1|x - 3| + 2) - 1| + 3) + 1)/(2(-2|(1|x - 3| + 2) - 1| + 3) + 3)) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-2(-1e^(-1(-5(-3|(-3x) + 3| + 1) - 3)) - 2))/(-1(-1e^(-1(-5(-3|(-3x) + 3| + 1) - 3)) - 2) + 3) and g(x) = (-2(-2(2((3x - 3)/(3x + 2)) + 3) + 5) - 1)/(1(-2(2((3x - 3)/(3x + 2)) + 3) + 5) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 2(3e^(-2((-3((-3(-3x^2 + 1x + 5) + 1)/(3(-3x^2 + 1x + 5) + 2)))/(1((-3(-3x^2 + 1x + 5) + 1)/(3(-3x^2 + 1x + 5) + 2)) - 3)))) - 1 and g(x) = -2|((2(-3|((-3x)/(2x - 1))| + 3) + 3)/(2(-3|((-3x)/(2x - 1))| + 3) + 1)) + 1| + 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1|((-2((2(2e^(-1(-1x)) + 2) + 2)/(-2(2e^(-1(-1x)) + 2) + 1)) - 3)/(3((2(2e^(-1(-1x)) + 2) + 2)/(-2(2e^(-1(-1x)) + 2) + 1)))) - 3| + 1 and g(x) = 3(-1(-1((3x + 1)/(2x + 3)) - 5) + 4) + 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 1(-2(3((-1(2x - 4) + 3)/(1(2x - 4) - 3)) - 3) + 3)^2 + 5(-2(3((-1(2x - 4) + 3)/(1(2x - 4) - 3)) - 3) + 3) - 5 and g(x) = 2(4(-3|(-4x + 4) + 3|)^2 - 1) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -2|(5(2(-5(3|x - 2| - 1)) - 4) - 1) - 3| and g(x) = -3|(1|((-1(2|x - 3| - 1) + 3)/(-1(2|x - 3| - 1) - 2)) - 2| - 3)| + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-2(-2(-4((3((-1x + 3)/(-2x - 2)) + 2)/(1((-1x + 3)/(-2x - 2))))^2 + 1((3((-1x + 3)/(-2x - 2)) + 2)/(1((-1x + 3)/(-2x - 2)))) + 2)^2 - 5(-4((3((-1x + 3)/(-2x - 2)) + 2)/(1((-1x + 3)/(-2x - 2))))^2 + 1((3((-1x + 3)/(-2x - 2)) + 2)/(1((-1x + 3)/(-2x - 2)))) + 2) + 5) - 2)/(-1(-2(-4((3((-1x + 3)/(-2x - 2)) + 2)/(1((-1x + 3)/(-2x - 2))))^2 + 1((3((-1x + 3)/(-2x - 2)) + 2)/(1((-1x + 3)/(-2x - 2)))) + 2)^2 - 5(-4((3((-1x + 3)/(-2x - 2)) + 2)/(1((-1x + 3)/(-2x - 2))))^2 + 1((3((-1x + 3)/(-2x - 2)) + 2)/(1((-1x + 3)/(-2x - 2)))) + 2) + 5) - 2) and g(x) = 3(-1(3cos(1\u03c0((3x + 3)/(2x + 1))) - 3) + 5) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-2(-1(-1(2|(4x^2 + 1x - 5)| - 3)^2 - 1(2|(4x^2 + 1x - 5)| - 3) + 4) + 3) - 2)/(-3(-1(-1(2|(4x^2 + 1x - 5)| - 3)^2 - 1(2|(4x^2 + 1x - 5)| - 3) + 4) + 3) - 2) and g(x) = (-1(-2(-5((-1x + 2)/(-3x + 4))^2 + 4((-1x + 2)/(-3x + 4)) + 4)^2 + 3) - 2)/(-2(-2(-5((-1x + 2)/(-3x + 4))^2 + 4((-1x + 2)/(-3x + 4)) + 4)^2 + 3)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4(3e^(-2(-3((2(-2x - 2) + 3)/(1(-2x - 2) + 1))^2 - 4((2(-2x - 2) + 3)/(1(-2x - 2) + 1)) + 5)) - 1) + 4 and g(x) = (-1(-3(1(-3sin(3\u03c0x + 2) + 3)^2 - 1(-3sin(3\u03c0x + 2) + 3) - 1)^2 - 2(1(-3sin(3\u03c0x + 2) + 3)^2 - 1(-3sin(3\u03c0x + 2) + 3) - 1) + 5) - 3)/(2(-3(1(-3sin(3\u03c0x + 2) + 3)^2 - 1(-3sin(3\u03c0x + 2) + 3) - 1)^2 - 2(1(-3sin(3\u03c0x + 2) + 3)^2 - 1(-3sin(3\u03c0x + 2) + 3) - 1) + 5) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-4((-1((-2(-2x + 5) + 2)/(-3(-2x + 5) - 3)) + 2)/(2((-2(-2x + 5) + 2)/(-3(-2x + 5) - 3)) + 2)) - 2) - 3 and g(x) = (-2((1(1|(1|x - 1| + 1) - 1| - 1) + 2)/(-1(1|(1|x - 1| + 1) - 1| - 1))) + 1)/(1((1(1|(1|x - 1| + 1) - 1| - 1) + 2)/(-1(1|(1|x - 1| + 1) - 1| - 1))) - 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -1|(1|((-2(4(1x^2 + 2) - 3) + 1)/(-3(4(1x^2 + 2) - 3) - 3)) + 2| + 1) - 1| + 3 and g(x) = 4((-1((-2((2x + 3)/(2x - 1)))/(-1((2x + 3)/(2x - 1)) - 3)) - 3)/(2((-2((2x + 3)/(2x - 1)))/(-1((2x + 3)/(2x - 1)) - 3))))^2 + 5((-1((-2((2x + 3)/(2x - 1)))/(-1((2x + 3)/(2x - 1)) - 3)) - 3)/(2((-2((2x + 3)/(2x - 1)))/(-1((2x + 3)/(2x - 1)) - 3)))) - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -5((-2(-2((-3(2|x + 2|) - 3)/(3(2|x + 2|) - 2)) + 2) + 1)/(1(-2((-3(2|x + 2|) - 3)/(3(2|x + 2|) - 2)) + 2) - 2)) - 4 and g(x) = 1((-1(-3|(-5x^2 - 1x - 2) + 1| - 1) + 3)/(2(-3|(-5x^2 - 1x - 2) + 1| - 1))) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1|(4(-1(-3(3x - 3) - 1)^2 - 3(-3(3x - 3) - 1))^2 - 4(-1(-3(3x - 3) - 1)^2 - 3(-3(3x - 3) - 1)) - 3) - 1| and g(x) = 4(-2|(3(-3e^(-1x) - 3)^2 + 3(-3e^(-1x) - 3))| + 2)^2 + 5(-2|(3(-3e^(-1x) - 3)^2 + 3(-3e^(-1x) - 3))| + 2) + 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3|((-1((-3((-3(-1x) - 2)/(-1(-1x) + 2)) + 2)/(-1((-3(-1x) - 2)/(-1(-1x) + 2)) - 1)) - 1)/(-2((-3((-3(-1x) - 2)/(-1(-1x) + 2)) + 2)/(-1((-3(-1x) - 2)/(-1(-1x) + 2)) - 1)) - 2)) + 2| - 1 and g(x) = (-1(2e^(-1(-1((-3x + 2)/(-2x + 3))^2 + 4((-3x + 2)/(-2x + 3)) + 4)) - 2) - 1)/(3(2e^(-1(-1((-3x + 2)/(-2x + 3))^2 + 4((-3x + 2)/(-2x + 3)) + 4)) - 2) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1|(2|((2(-1cos(2\u03c0(5x^2 + 4x + 5)) + 3) - 1)/(2(-1cos(2\u03c0(5x^2 + 4x + 5)) + 3) - 1)) - 1| + 1) + 1| + 3 and g(x) = (-1((-1((-3(-5x + 4) - 1)/(3(-5x + 4))) - 1)/(-1((-3(-5x + 4) - 1)/(3(-5x + 4))))) - 3)/(3((-1((-3(-5x + 4) - 1)/(3(-5x + 4))) - 1)/(-1((-3(-5x + 4) - 1)/(3(-5x + 4))))) + 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 1(1(-4(-4(-2|x - 1| + 1)^2 - 1(-2|x - 1| + 1)) - 5) - 3) + 5 and g(x) = -1((1((-1(1|x + 3| - 3) + 1)/(1(1|x + 3| - 3))) - 3)/(3((-1(1|x + 3| - 3) + 1)/(1(1|x + 3| - 3))) - 2)) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-1(2|(-4((1((-2x)/(-1x - 2)) - 1)/(3((-2x)/(-1x - 2)) + 3))^2 + 5((1((-2x)/(-1x - 2)) - 1)/(3((-2x)/(-1x - 2)) + 3)) + 2) + 2| - 3) + 1)/(-2(2|(-4((1((-2x)/(-1x - 2)) - 1)/(3((-2x)/(-1x - 2)) + 3))^2 + 5((1((-2x)/(-1x - 2)) - 1)/(3((-2x)/(-1x - 2)) + 3)) + 2) + 2| - 3) - 3) and g(x) = 1|((-3(5(-1|x + 3| - 2)^2 - 2(-1|x + 3| - 2) - 2))/(2(5(-1|x + 3| - 2)^2 - 2(-1|x + 3| - 2) - 2) - 1)) - 2| - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3sin(3\u03c0((-2(-5(3(-2x^2 + 3x + 5) + 2)^2 - 5(3(-2x^2 + 3x + 5) + 2) - 5) - 3)/(3(-5(3(-2x^2 + 3x + 5) + 2)^2 - 5(3(-2x^2 + 3x + 5) + 2) - 5) - 2)) + 3) + 1 and g(x) = 5(3(1((-2x + 3)/(-3x + 4)) - 4) + 2) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (3(-1(-4(-1(-1x - 3) + 1) + 5)^2 + 2(-4(-1(-1x - 3) + 1) + 5) + 1) + 1)/(-1(-1(-4(-1(-1x - 3) + 1) + 5)^2 + 2(-4(-1(-1x - 3) + 1) + 5) + 1) - 2) and g(x) = -2|(-3e^(-1(-2(1x - 2)^2 - 1(1x - 2) + 2)) - 1) + 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (1(-3((3(3|(-3x + 4) + 3| - 1) - 3)/(-2(3|(-3x + 4) + 3| - 1))) - 3) - 3)/(2(-3((3(3|(-3x + 4) + 3| - 1) - 3)/(-2(3|(-3x + 4) + 3| - 1))) - 3) - 1) and g(x) = 1|(-2((-1(1|x - 1|) + 2)/(3(1|x - 1|) + 3))^2 - 1((-1(1|x - 1|) + 2)/(3(1|x - 1|) + 3)) + 1) + 2| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2|(1(4(-1|((-2x + 2)/(2x + 2)) + 1| + 2) + 4) + 2) + 3| + 2 and g(x) = 1((3(-1((-2x + 3)/(-3x + 2)) - 4) + 1)/(-1(-1((-2x + 3)/(-3x + 2)) - 4) - 1)) + 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(-2|(2e^(2(1(1x - 2) - 1)) - 2) - 3|) - 1 and g(x) = 3|(1|(-3e^(1((-2x - 3)/(-1x))))| + 3) + 3| - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3((1(-2|(-3|(-5x - 4) - 1|) + 3| + 2) - 3)/(3(-2|(-3|(-5x - 4) - 1|) + 3| + 2) + 1)) + 2 and g(x) = -1((-3((-2(-1sin(1\u03c0x - 1) - 1) - 3)/(-1(-1sin(1\u03c0x - 1) - 1) + 3)))/(1((-2(-1sin(1\u03c0x - 1) - 1) - 3)/(-1(-1sin(1\u03c0x - 1) - 1) + 3)) + 1)) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (2(-3(-1|(4(1cos(1\u03c0x - 1) + 3) + 3) + 2| + 3)^2 + 4(-1|(4(1cos(1\u03c0x - 1) + 3) + 3) + 2| + 3) - 4) + 3)/(3(-3(-1|(4(1cos(1\u03c0x - 1) + 3) + 3) + 2| + 3)^2 + 4(-1|(4(1cos(1\u03c0x - 1) + 3) + 3) + 2| + 3) - 4)) and g(x) = 1(2(4(4x^2 - 5x - 1) - 5) + 5) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -4(-3((1(1|(-5x^2 + 1) + 3|) + 2)/(-3(1|(-5x^2 + 1) + 3|) - 3)) + 5)^2 + 5(-3((1(1|(-5x^2 + 1) + 3|) + 2)/(-3(1|(-5x^2 + 1) + 3|) - 3)) + 5) + 3 and g(x) = 1(-1(1((1x + 2)/(-1x - 1))^2 - 3((1x + 2)/(-1x - 1)))^2 - 3(1((1x + 2)/(-1x - 1))^2 - 3((1x + 2)/(-1x - 1))) - 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -5(3(-4((-2(2sin(1\u03c0x + 3) + 3) - 1)/(3(2sin(1\u03c0x + 3) + 3) + 1)) + 3)^2 + 5(-4((-2(2sin(1\u03c0x + 3) + 3) - 1)/(3(2sin(1\u03c0x + 3) + 3) + 1)) + 3) + 5) - 4 and g(x) = (-1(2|(1|(-4x^2 + 5x + 2) - 3| + 3) - 2| - 1) - 3)/(-1(2|(1|(-4x^2 + 5x + 2) - 3| + 3) - 2| - 1) + 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2|(-2cos(2\u03c0((2(-2((-1x - 3)/(-2x + 3)) - 1) - 1)/(2(-2((-1x - 3)/(-2x + 3)) - 1) - 1))) - 3) + 1| - 1 and g(x) = 1|(4(-2|((-2x)/(-1x + 2))|)^2 + 2(-2|((-2x)/(-1x + 2))|)) - 1| meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -3(-3|(2(-2((2x + 3)/(-2x + 3)) + 5) - 2) + 1| - 2)^2 - 3(-3|(2(-2((2x + 3)/(-2x + 3)) + 5) - 2) + 1| - 2) and g(x) = -1|(3(2sin(2\u03c0(-2x^2 - 5)) + 2) - 3) - 3| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (3(-2(-5((1(1x^2 + 1x - 3) + 1)/(-1(1x^2 + 1x - 3)))^2 - 2((1(1x^2 + 1x - 3) + 1)/(-1(1x^2 + 1x - 3))) - 4) - 3) + 1)/(3(-2(-5((1(1x^2 + 1x - 3) + 1)/(-1(1x^2 + 1x - 3)))^2 - 2((1(1x^2 + 1x - 3) + 1)/(-1(1x^2 + 1x - 3))) - 4) - 3) - 2) and g(x) = -1(-2(2e^(-2((1x + 3)/(1x))) - 1)^2 - 4(2e^(-2((1x + 3)/(1x))) - 1) + 1) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2(-3|((-3((1(2|x - 3| - 2))/(3(2|x - 3| - 2) + 2)))/(2((1(2|x - 3| - 2))/(3(2|x - 3| - 2) + 2)) + 2)) - 1|)^2 + 1(-3|((-3((1(2|x - 3| - 2))/(3(2|x - 3| - 2) + 2)))/(2((1(2|x - 3| - 2))/(3(2|x - 3| - 2) + 2)) + 2)) - 1|) + 3 and g(x) = (1((1(-3(3x^2 + 1x + 1) + 4) + 1)/(3(-3(3x^2 + 1x + 1) + 4) - 2)) - 3)/(-1((1(-3(3x^2 + 1x + 1) + 4) + 1)/(3(-3(3x^2 + 1x + 1) + 4) - 2)) + 2) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(2(-2|(-5(-3cos(1\u03c0x + 1) + 2) + 3) - 2| + 2)^2 + 2(-2|(-5(-3cos(1\u03c0x + 1) + 2) + 3) - 2| + 2) + 2) - 1)/(3(2(-2|(-5(-3cos(1\u03c0x + 1) + 2) + 3) - 2| + 2)^2 + 2(-2|(-5(-3cos(1\u03c0x + 1) + 2) + 3) - 2| + 2) + 2)) and g(x) = (-2(-2(2e^(2(3|x + 2| - 3)) - 2)) - 2)/(1(-2(2e^(2(3|x + 2| - 3)) - 2)) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -3|(3(-2sin(1\u03c0((-1(-3x + 5) + 1)/(1(-3x + 5) + 3))) + 3) - 5) + 3| - 2 and g(x) = -3e^(-2(-1(1(-5x + 1) + 3)^2 - 1(1(-5x + 1) + 3) + 3)) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (2((3((-2(-3(-4x + 3)^2 + 5(-4x + 3) - 1) + 3)/(-1(-3(-4x + 3)^2 + 5(-4x + 3) - 1) + 3)) + 1)/(2((-2(-3(-4x + 3)^2 + 5(-4x + 3) - 1) + 3)/(-1(-3(-4x + 3)^2 + 5(-4x + 3) - 1) + 3)) - 3)) - 1)/(-1((3((-2(-3(-4x + 3)^2 + 5(-4x + 3) - 1) + 3)/(-1(-3(-4x + 3)^2 + 5(-4x + 3) - 1) + 3)) + 1)/(2((-2(-3(-4x + 3)^2 + 5(-4x + 3) - 1) + 3)/(-1(-3(-4x + 3)^2 + 5(-4x + 3) - 1) + 3)) - 3)) - 2) and g(x) = -3(-3(-2|(-2|x - 2| + 3) - 1|)^2) + 5 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-1(1((-1(2|(3e^(1x) - 2)| - 1) - 3)/(-1(2|(3e^(1x) - 2)| - 1) - 1))^2 - 2((-1(2|(3e^(1x) - 2)| - 1) - 3)/(-1(2|(3e^(1x) - 2)| - 1) - 1)) - 1) - 1)/(-1(1((-1(2|(3e^(1x) - 2)| - 1) - 3)/(-1(2|(3e^(1x) - 2)| - 1) - 1))^2 - 2((-1(2|(3e^(1x) - 2)| - 1) - 3)/(-1(2|(3e^(1x) - 2)| - 1) - 1)) - 1)) and g(x) = -2|(3(1|((1x - 2)/(1x + 1))| - 1)^2 - 2) - 2| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1|(-3|((-2((-3(2cos(2\u03c0x - 3) - 2) + 1)/(-1(2cos(2\u03c0x - 3) - 2) + 3)) - 2)/(3((-3(2cos(2\u03c0x - 3) - 2) + 1)/(-1(2cos(2\u03c0x - 3) - 2) + 3)) + 2)) - 3|) + 3| and g(x) = -1((-3((-2((-3x)/(-1x - 2)))/(3((-3x)/(-1x - 2)) + 2)) + 2)/(3((-2((-3x)/(-1x - 2)))/(3((-3x)/(-1x - 2)) + 2)) - 1))^2 + 3((-3((-2((-3x)/(-1x - 2)))/(3((-3x)/(-1x - 2)) + 2)) + 2)/(3((-2((-3x)/(-1x - 2)))/(3((-3x)/(-1x - 2)) + 2)) - 1)) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -2((-2(-2((3(-3x - 4) - 3)/(1(-3x - 4))) + 1) + 3)/(-1(-2((3(-3x - 4) - 3)/(1(-3x - 4))) + 1)))^2 - 1((-2(-2((3(-3x - 4) - 3)/(1(-3x - 4))) + 1) + 3)/(-1(-2((3(-3x - 4) - 3)/(1(-3x - 4))) + 1))) and g(x) = -1cos(3\u03c0((-2((3((-2x + 1)/(-2x - 1)) - 2)/(3((-2x + 1)/(-2x - 1)) + 2)) + 3)/(-2((3((-2x + 1)/(-2x - 1)) - 2)/(3((-2x + 1)/(-2x - 1)) + 2)) - 1)) + 2) - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3((1(1((1(3x + 5) + 2)/(3(3x + 5) + 2)) + 1) + 2)/(3(1((1(3x + 5) + 2)/(3(3x + 5) + 2)) + 1) - 2)) + 3)/(-3((1(1((1(3x + 5) + 2)/(3(3x + 5) + 2)) + 1) + 2)/(3(1((1(3x + 5) + 2)/(3(3x + 5) + 2)) + 1) - 2)) - 2) and g(x) = (1(1(3|(1x + 5) - 3| - 1) - 1) + 3)/(-1(1(3|(1x + 5) - 3| - 1) - 1) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-2(-1|(-2sin(1\u03c0((1((1x + 3)/(-2x)))/(-1((1x + 3)/(-2x)))) + 1) - 3) + 2| + 2) - 2)/(-3(-1|(-2sin(1\u03c0((1((1x + 3)/(-2x)))/(-1((1x + 3)/(-2x)))) + 1) - 3) + 2| + 2) - 1) and g(x) = 1|((-2((1((-2x + 3)/(3x - 2)) - 3)/(-2((-2x + 3)/(3x - 2)) + 1)) + 3)/(-3((1((-2x + 3)/(3x - 2)) - 3)/(-2((-2x + 3)/(3x - 2)) + 1)) + 4)) + 1| - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 4((1(5((1((2x + 2)/(-2x - 1)) - 2)/(2((2x + 2)/(-2x - 1)) + 3)) - 3) - 2)/(1(5((1((2x + 2)/(-2x - 1)) - 2)/(2((2x + 2)/(-2x - 1)) + 3)) - 3) + 1)) - 5 and g(x) = -1|(1((-1(-2x - 5) + 1)/(-3(-2x - 5) - 1))^2 - 5((-1(-2x - 5) + 1)/(-3(-2x - 5) - 1)) + 3) + 1| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = -4(-1(-2|(-1(5x^2 - 5x - 1) - 1)| + 1) + 3)^2 + 4(-1(-2|(-1(5x^2 - 5x - 1) - 1)| + 1) + 3) - 3 and g(x) = 2(4(1|(-2x^2 - 1x + 4)| - 2) - 3) + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-3((1(1e^(2(-3(3x + 2) - 2)) - 1) - 2)/(3(1e^(2(-3(3x + 2) - 2)) - 1) + 3)) - 3)/(-1((1(1e^(2(-3(3x + 2) - 2)) - 1) - 2)/(3(1e^(2(-3(3x + 2) - 2)) - 1) + 3)) - 3) and g(x) = 1(3(-1(-5x + 1) + 5) - 4) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -4((-2((-2(-5(-1x - 5)^2 + 2(-1x - 5) - 1))/(3(-5(-1x - 5)^2 + 2(-1x - 5) - 1) - 1)) - 2)/(-1((-2(-5(-1x - 5)^2 + 2(-1x - 5) - 1))/(3(-5(-1x - 5)^2 + 2(-1x - 5) - 1) - 1)) + 3))^2 - 1((-2((-2(-5(-1x - 5)^2 + 2(-1x - 5) - 1))/(3(-5(-1x - 5)^2 + 2(-1x - 5) - 1) - 1)) - 2)/(-1((-2(-5(-1x - 5)^2 + 2(-1x - 5) - 1))/(3(-5(-1x - 5)^2 + 2(-1x - 5) - 1) - 1)) + 3)) - 3 and g(x) = (2((-1((-2(5x^2 + 4x) + 1)/(2(5x^2 + 4x))) + 3)/(-1((-2(5x^2 + 4x) + 1)/(2(5x^2 + 4x))) + 2)) - 1)/(1((-1((-2(5x^2 + 4x) + 1)/(2(5x^2 + 4x))) + 3)/(-1((-2(5x^2 + 4x) + 1)/(2(5x^2 + 4x))) + 2))) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(-2sin(1\u03c0(-1|((-3(-1|x + 2| - 2) + 1)/(1(-1|x + 2| - 2) - 2))| - 3))) + 2| - 1 and g(x) = 5((1((1(-3|x - 2|) + 3)/(-2(-3|x - 2|))) - 1)/(3((1(-3|x - 2|) + 3)/(-2(-3|x - 2|))))) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2|(-3(1sin(2\u03c0(5((2x - 3)/(1x + 3))^2 - 1((2x - 3)/(1x + 3)) - 5) - 2) + 2) - 2)| - 1 and g(x) = 3(2e^(-2((2(-2x^2 - 4x + 4) - 2)/(3(-2x^2 - 4x + 4) - 2))))^2 - 1(2e^(-2((2(-2x^2 - 4x + 4) - 2)/(3(-2x^2 - 4x + 4) - 2)))) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (-3(2cos(1\u03c0(-2(1(5x^2 + 5x + 4)^2 + 5(5x^2 + 5x + 4) + 4) + 1) + 2) - 3) - 3)/(-2(2cos(1\u03c0(-2(1(5x^2 + 5x + 4)^2 + 5(5x^2 + 5x + 4) + 4) + 1) + 2) - 3) - 2) and g(x) = -1|((-1((-2(-5x + 2) + 1)/(3(-5x + 2))) + 2)/(3((-2(-5x + 2) + 1)/(3(-5x + 2))))) + 1| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(1(-2(-4(1|x + 1|) + 2) - 3)^2 + 4(-2(-4(1|x + 1|) + 2) - 3) + 3)^2 + 4(1(-2(-4(1|x + 1|) + 2) - 3)^2 + 4(-2(-4(1|x + 1|) + 2) - 3) + 3) + 1 and g(x) = -1(-3|(-3(3|x - 3| + 2)^2 + 1(3|x - 3| + 2) + 5) - 2| - 1) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1(2cos(1\u03c0((-1((-3(-3|x + 1| + 1))/(3(-3|x + 1| + 1))) + 1)/(2((-3(-3|x + 1| + 1))/(3(-3|x + 1| + 1))) + 2)) - 1) + 2) + 1 and g(x) = -4(-1|((-1(4x^2 - 5x - 5) + 3)/(2(4x^2 - 5x - 5) + 1)) - 2| + 2) + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -3cos(3\u03c0(1(-2|(-3(1x - 4)^2 + 3(1x - 4) + 1) + 1| - 3) + 5) + 3) - 1 and g(x) = 3|(-2((1(2cos(3\u03c0x + 2) - 2))/(-2(2cos(3\u03c0x + 2) - 2) + 1))) + 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (1(1(3|((1((1x)/(3x + 3)) + 2)/(2((1x)/(3x + 3)) - 1)) + 2| - 2)^2 - 1(3|((1((1x)/(3x + 3)) + 2)/(2((1x)/(3x + 3)) - 1)) + 2| - 2) - 4) + 2)/(-3(1(3|((1((1x)/(3x + 3)) + 2)/(2((1x)/(3x + 3)) - 1)) + 2| - 2)^2 - 1(3|((1((1x)/(3x + 3)) + 2)/(2((1x)/(3x + 3)) - 1)) + 2| - 2) - 4) + 1) and g(x) = 1|(5(-1cos(1\u03c0(-5x - 3) + 1) - 1) + 1) - 2| + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5(2|(1e^(2(-1(2x^2 - 3x - 3) - 3)) + 2) - 2| - 1) + 2 and g(x) = -2e^(1((-1(5(-1|x - 1|)^2 + 1(-1|x - 1|) - 4) + 3)/(-3(5(-1|x - 1|)^2 + 1(-1|x - 1|) - 4)))) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(3(-1((2((1x + 2)/(1x)) + 2)/(1((1x + 2)/(1x)) + 1))^2 - 2((2((1x + 2)/(1x)) + 2)/(1((1x + 2)/(1x)) + 1)) - 2)) - 1)/(1(3(-1((2((1x + 2)/(1x)) + 2)/(1((1x + 2)/(1x)) + 1))^2 - 2((2((1x + 2)/(1x)) + 2)/(1((1x + 2)/(1x)) + 1)) - 2)) + 2) and g(x) = 1(4((3((1x)/(-1x + 2)) + 3)/(-3((1x)/(-1x + 2)) - 1)) - 1) + 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -5((-3(-1(-1((3x + 2)/(-3x - 3)) - 3) - 2))/(-2(-1(-1((3x + 2)/(-3x - 3)) - 3) - 2) - 1))^2 + 3((-3(-1(-1((3x + 2)/(-3x - 3)) - 3) - 2))/(-2(-1(-1((3x + 2)/(-3x - 3)) - 3) - 2) - 1)) + 4 and g(x) = -2|(5((-1(1e^(-2x) + 1))/(2(1e^(-2x) + 1) - 1))^2 - 1((-1(1e^(-2x) + 1))/(2(1e^(-2x) + 1) - 1)) + 3) - 3| - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (2((1(2|(-1(2e^(-1x) - 2) - 2) + 3| - 3) + 3)/(-1(2|(-1(2e^(-1x) - 2) - 2) + 3| - 3) - 3)) - 2)/(1((1(2|(-1(2e^(-1x) - 2) - 2) + 3| - 3) + 3)/(-1(2|(-1(2e^(-1x) - 2) - 2) + 3| - 3) - 3)) - 3) and g(x) = 4((-1(3(3|x - 3|) - 2) - 3)/(-2(3(3|x - 3|) - 2) + 1)) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-1|(1(2e^(-1((1x - 1)/(-2x - 1))) - 3)^2 - 2(2e^(-1((1x - 1)/(-2x - 1))) - 3) - 3) + 1| + 2) - 1 and g(x) = (-3((-2(-2e^(-1(-4x + 5)) + 1) - 3)/(-1(-2e^(-1(-4x + 5)) + 1) + 2)) - 2)/(-1((-2(-2e^(-1(-4x + 5)) + 1) - 3)/(-1(-2e^(-1(-4x + 5)) + 1) + 2)) - 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1|(-2sin(1\u03c0(1(3(-1|x - 3| - 1)^2 + 5(-1|x - 3| - 1) + 3))) - 3) + 1| + 3 and g(x) = 1|(-1(3e^(1(4x)) - 3)^2 - 4(3e^(1(4x)) - 3) - 1) + 1| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (1(-2((-2(2cos(2\u03c0(-1x) - 2) - 2) + 1)/(-1(2cos(2\u03c0(-1x) - 2) - 2) - 3)) - 3) + 3)/(1(-2((-2(2cos(2\u03c0(-1x) - 2) - 2) + 1)/(-1(2cos(2\u03c0(-1x) - 2) - 2) - 3)) - 3) + 1) and g(x) = 5(2(-3(4x + 1)^2 + 3(4x + 1) + 2)^2 - 4(-3(4x + 1)^2 + 3(4x + 1) + 2) - 3)^2 + 2(2(-3(4x + 1)^2 + 3(4x + 1) + 2)^2 - 4(-3(4x + 1)^2 + 3(4x + 1) + 2) - 3) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (2(3(-1|(-3(-1x + 3)^2 + 5(-1x + 3) - 4) + 3| + 3) - 2) - 3)/(3(3(-1|(-3(-1x + 3)^2 + 5(-1x + 3) - 4) + 3| + 3) - 2) - 2) and g(x) = -5(-1(1|(3x) + 2| - 3)^2 + 3(1|(3x) + 2| - 3) - 1) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3|(3(2|(1((-1x + 3)/(2x + 3))) + 2|)^2 - 4(2|(1((-1x + 3)/(2x + 3))) + 2|) - 2) + 2| - 1 and g(x) = 1|(4(-1(3x^2 + 1x + 3)^2 - 1)^2 + 3(-1(3x^2 + 1x + 3)^2 - 1) - 2) + 1| + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -3(3|((-3(-4(-5x^2 - 4x + 5)) + 3)/(3(-4(-5x^2 - 4x + 5)) + 1)) - 3| - 3)^2 + 5(3|((-3(-4(-5x^2 - 4x + 5)) + 3)/(3(-4(-5x^2 - 4x + 5)) + 1)) - 3| - 3) - 2 and g(x) = -2(-5(-3|(-1|x + 1| - 3)|) - 4)^2 + 5(-5(-3|(-1|x + 1| - 3)|) - 4) - 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -1((-3(-3((-1(2e^(1x) - 3) + 3)/(2(2e^(1x) - 3) - 1))^2 - 4((-1(2e^(1x) - 3) + 3)/(2(2e^(1x) - 3) - 1)) + 2) + 3)/(1(-3((-1(2e^(1x) - 3) + 3)/(2(2e^(1x) - 3) - 1))^2 - 4((-1(2e^(1x) - 3) + 3)/(2(2e^(1x) - 3) - 1)) + 2) + 2)) + 3 and g(x) = 3|(-5(-2((-3x + 3)/(-1x + 3)) - 5)^2 - 5(-2((-3x + 3)/(-1x + 3)) - 5) - 2) + 3| - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 5(3(-3|((-2(-3x + 4) + 2)/(-2(-3x + 4) + 1)) - 1| - 3) - 4)^2 + 2(3(-3|((-2(-3x + 4) + 2)/(-2(-3x + 4) + 1)) - 1| - 3) - 4) + 4 and g(x) = 3|(1|((-1((-3x)/(-3x + 2)) + 3)/(1((-3x)/(-3x + 2)) + 1)) - 2|)| + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2(-5((-2((1(-4x) + 2)/(1(-4x) + 1)) + 1)/(1((1(-4x) + 2)/(1(-4x) + 1)) + 2))^2 + 4((-2((1(-4x) + 2)/(1(-4x) + 1)) + 1)/(1((1(-4x) + 2)/(1(-4x) + 1)) + 2)) + 1) + 5 and g(x) = 5(5((2(-2x + 1) + 2)/(-2(-2x + 1) - 1)) - 4)^2 + 1(5((2(-2x + 1) + 2)/(-2(-2x + 1) - 1)) - 4) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 2|(-1|((2(1((-1x - 2)/(-2x - 3)) - 3))/(1(1((-1x - 2)/(-2x - 3)) - 3) + 2)) + 2| - 3)| and g(x) = (3((-2(-3|(-5x + 4) + 3| + 1) - 1)/(-2(-3|(-5x + 4) + 3| + 1) + 3)) - 1)/(2((-2(-3|(-5x + 4) + 3| + 1) - 1)/(-2(-3|(-5x + 4) + 3| + 1) + 3))) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1(5((-3(-2((1x + 2)/(-2x - 3)) + 2) - 3)/(3(-2((1x + 2)/(-2x - 3)) + 2) + 2))^2 + 1)^2 - 2(5((-3(-2((1x + 2)/(-2x - 3)) + 2) - 3)/(3(-2((1x + 2)/(-2x - 3)) + 2) + 2))^2 + 1) - 2 and g(x) = -2|(3|(-2e^(-2(3|x + 2| + 2))) - 3| + 2) - 1| - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2(2e^(-1(-3((1(3x + 3) - 3)/(-3(3x + 3) + 2))^2 - 4((1(3x + 3) - 3)/(-3(3x + 3) + 2)) + 4)) + 2) + 5 and g(x) = 1sin(1\u03c0(-1(-1(1|x - 3| - 2)^2 + 4(1|x - 3| - 2) + 1) - 1) + 1) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 4(4((3(-5(5x^2 + 1x + 2) - 4) + 2)/(2(-5(5x^2 + 1x + 2) - 4) + 3)) + 1)^2 + 1(4((3(-5(5x^2 + 1x + 2) - 4) + 2)/(2(-5(5x^2 + 1x + 2) - 4) + 3)) + 1) + 1 and g(x) = 2((1(-2(1x + 2) - 2) - 3)/(-3(-2(1x + 2) - 2) + 1)) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (3(-1(-2(-5(3x - 2) - 3)^2 - 2(-5(3x - 2) - 3) - 2) + 1) + 1)/(3(-1(-2(-5(3x - 2) - 3)^2 - 2(-5(3x - 2) - 3) - 2) + 1) - 2) and g(x) = 2((-1(-1(-1x + 5)) - 3)/(-2(-1(-1x + 5)) + 3))^2 + 5((-1(-1(-1x + 5)) - 3)/(-2(-1(-1x + 5)) + 3)) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 5((-1(5(2(1x + 1)^2 - 4(1x + 1) - 5)^2 + 4(2(1x + 1)^2 - 4(1x + 1) - 5) - 3) - 2)/(-1(5(2(1x + 1)^2 - 4(1x + 1) - 5)^2 + 4(2(1x + 1)^2 - 4(1x + 1) - 5) - 3) + 2)) - 5 and g(x) = (-1(5(5((-3x + 3)/(-1x + 2))^2 + 5((-3x + 3)/(-1x + 2)) - 1) - 2) - 1)/(2(5(5((-3x + 3)/(-1x + 2))^2 + 5((-3x + 3)/(-1x + 2)) - 1) - 2) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-2((-1(1(-5(-2x + 5)^2 - 3(-2x + 5)) + 2) + 2)/(1(1(-5(-2x + 5)^2 - 3(-2x + 5)) + 2) - 3)) + 2)/(-2((-1(1(-5(-2x + 5)^2 - 3(-2x + 5)) + 2) + 2)/(1(1(-5(-2x + 5)^2 - 3(-2x + 5)) + 2) - 3)) + 3) and g(x) = (3(-2((-2(-5x + 5) + 1)/(3(-5x + 5)))) - 1)/(-3(-2((-2(-5x + 5) + 1)/(3(-5x + 5)))) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -1(3|((2(3|((-2x - 2)/(2x)) + 1|) + 1)/(-3(3|((-2x - 2)/(2x)) + 1|) + 1)) + 1|)^2 - 1(3|((2(3|((-2x - 2)/(2x)) + 1|) + 1)/(-3(3|((-2x - 2)/(2x)) + 1|) + 1)) + 1|) + 2 and g(x) = (-3(-1(1sin(3\u03c0((-1x + 2)/(-1x - 3)) + 1) - 1)^2 + 4(1sin(3\u03c0((-1x + 2)/(-1x - 3)) + 1) - 1) - 1) + 1)/(2(-1(1sin(3\u03c0((-1x + 2)/(-1x - 3)) + 1) - 1)^2 + 4(1sin(3\u03c0((-1x + 2)/(-1x - 3)) + 1) - 1) - 1) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(2|((-3(-1(3x^2 - 3x + 4)^2 + 5(3x^2 - 3x + 4) - 2) + 2)/(1(-1(3x^2 - 3x + 4)^2 + 5(3x^2 - 3x + 4) - 2) - 3)) + 1| - 3) - 2 and g(x) = -5(-2sin(3\u03c0(-1(-1x^2 + 2x - 4) + 1) + 1) - 3)^2 - 5(-2sin(3\u03c0(-1(-1x^2 + 2x - 4) + 1) + 1) - 3) - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-1((1(2(-4(-3|x - 2| - 1) + 1)^2 + 4(-4(-3|x - 2| - 1) + 1) - 5) + 2)/(2(2(-4(-3|x - 2| - 1) + 1)^2 + 4(-4(-3|x - 2| - 1) + 1) - 5) - 1)) - 1)/(2((1(2(-4(-3|x - 2| - 1) + 1)^2 + 4(-4(-3|x - 2| - 1) + 1) - 5) + 2)/(2(2(-4(-3|x - 2| - 1) + 1)^2 + 4(-4(-3|x - 2| - 1) + 1) - 5) - 1)) - 3) and g(x) = 5(-4((1(-2x + 2) - 3)/(-2(-2x + 2) - 2)) - 5)^2 - 5(-4((1(-2x + 2) - 3)/(-2(-2x + 2) - 2)) - 5) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 5(-2(2|((-3(3|x - 2| - 1))/(2(3|x - 2| - 1) - 1)) + 1| + 3)^2 + 1(2|((-3(3|x - 2| - 1))/(2(3|x - 2| - 1) - 1)) + 1| + 3) - 2)^2 - 2(-2(2|((-3(3|x - 2| - 1))/(2(3|x - 2| - 1) - 1)) + 1| + 3)^2 + 1(2|((-3(3|x - 2| - 1))/(2(3|x - 2| - 1) - 1)) + 1| + 3) - 2) - 3 and g(x) = 3|(-2e^(-1(-1((2x - 2)/(2x - 3)) + 4)) - 1)| meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2(-1(2|(1|((-3x - 3)/(-2x)) - 2|)| + 3) - 2)^2 - 2(-1(2|(1|((-3x - 3)/(-2x)) - 2|)| + 3) - 2) + 4 and g(x) = 3(4(4(3e^(1x) + 1) + 5)^2 + 3(4(3e^(1x) + 1) + 5) + 3) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-2((3(3e^(-2(4(1x^2 + 5x + 3)^2 + 3(1x^2 + 5x + 3) - 1)) - 1))/(-1(3e^(-2(4(1x^2 + 5x + 3)^2 + 3(1x^2 + 5x + 3) - 1)) - 1))))/(1((3(3e^(-2(4(1x^2 + 5x + 3)^2 + 3(1x^2 + 5x + 3) - 1)) - 1))/(-1(3e^(-2(4(1x^2 + 5x + 3)^2 + 3(1x^2 + 5x + 3) - 1)) - 1))) - 3) and g(x) = -5(1e^(1(5((-2x)/(-3x - 2))^2 + 4((-2x)/(-3x - 2)) + 2)) - 3)^2 - 3(1e^(1(5((-2x)/(-3x - 2))^2 + 4((-2x)/(-3x - 2)) + 2)) - 3) + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1|(3|(5((-3(2|x| + 1) + 3)/(-1(2|x| + 1) - 1))^2 + 2((-3(2|x| + 1) + 3)/(-1(2|x| + 1) - 1)) + 1) + 2| - 2) - 2| - 1 and g(x) = (2(-1(1((-3x - 1)/(-3x + 2)) + 3)^2 - 2(1((-3x - 1)/(-3x + 2)) + 3) - 1))/(2(-1(1((-3x - 1)/(-3x + 2)) + 3)^2 - 2(1((-3x - 1)/(-3x + 2)) + 3) - 1) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 5(1(-2e^(-1((-3(-3|x - 2|) + 3)/(1(-3|x - 2|) + 3))) - 1) + 2) + 4 and g(x) = 2|(-5(1(1|x + 2| + 3) - 5)^2 + 5(1(1|x + 2| + 3) - 5) + 1) - 3| - 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-2(1|(-5(-1cos(3\u03c0(5x - 5)) - 1)^2 - 5(-1cos(3\u03c0(5x - 5)) - 1) - 3)| + 2))/(-2(1|(-5(-1cos(3\u03c0(5x - 5)) - 1)^2 - 5(-1cos(3\u03c0(5x - 5)) - 1) - 3)| + 2) - 3) and g(x) = (-3(-1(3e^(1(1x^2 - 1)) - 2)) - 2)/(1(-1(3e^(1(1x^2 - 1)) - 2))) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3(2(-3|((-2(5x - 4) - 1)/(2(5x - 4) + 2)) + 1| + 2)^2 - 1(-3|((-2(5x - 4) - 1)/(2(5x - 4) + 2)) + 1| + 2) - 5) - 2 and g(x) = 1e^(-1(-3|((2((-2x + 2)/(-2x - 1)) + 3)/(-3((-2x + 2)/(-2x - 1)) + 2)) - 1| - 1)) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3(-4(3((2((2x - 1)/(3x - 2)) + 2)/(-3((2x - 1)/(3x - 2)))) - 1) + 1) - 5 and g(x) = -4(1|(-4((-2x + 2)/(1x))^2 - 4((-2x + 2)/(1x)) + 5) - 3| + 1)^2 + 2(1|(-4((-2x + 2)/(1x))^2 - 4((-2x + 2)/(1x)) + 5) - 3| + 1) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 3|((3(2(-3cos(3\u03c0(2x - 5) + 1) - 2)^2 + 1(-3cos(3\u03c0(2x - 5) + 1) - 2) - 5) + 1)/(2(2(-3cos(3\u03c0(2x - 5) + 1) - 2)^2 + 1(-3cos(3\u03c0(2x - 5) + 1) - 2) - 5) - 1)) + 1| + 1 and g(x) = 3|(5(-3(1sin(1\u03c0x + 3) - 2)^2 - 5) - 1) - 3| + 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3|(5(1|(2cos(1\u03c0((3x + 3)/(-2x + 3)) + 2) + 2) + 1| - 3)^2 - 2(1|(2cos(1\u03c0((3x + 3)/(-2x + 3)) + 2) + 2) + 1| - 3) - 5) + 1| and g(x) = (-2(5(-2((-1x - 1)/(1x - 2))^2 + 5((-1x - 1)/(1x - 2)) + 4)^2 - 2(-2((-1x - 1)/(1x - 2))^2 + 5((-1x - 1)/(1x - 2)) + 4) - 5) + 3)/(1(5(-2((-1x - 1)/(1x - 2))^2 + 5((-1x - 1)/(1x - 2)) + 4)^2 - 2(-2((-1x - 1)/(1x - 2))^2 + 5((-1x - 1)/(1x - 2)) + 4) - 5) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 3(-1(4((1((-1x + 3)/(3x - 2)) - 2)/(-1((-1x + 3)/(3x - 2)))) + 5) - 5) + 3 and g(x) = (-3(-4(1sin(1\u03c0(-1x^2 - 2x - 2) - 3) - 3)^2 - 5(1sin(1\u03c0(-1x^2 - 2x - 2) - 3) - 3) + 4) - 1)/(2(-4(1sin(1\u03c0(-1x^2 - 2x - 2) - 3) - 3)^2 - 5(1sin(1\u03c0(-1x^2 - 2x - 2) - 3) - 3) + 4)) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -4(-2sin(3\u03c0(2((-1(-5x^2 - 2x - 5) + 2)/(3(-5x^2 - 2x - 5) + 1)) - 1) + 3) + 1)^2 + 3(-2sin(3\u03c0(2((-1(-5x^2 - 2x - 5) + 2)/(3(-5x^2 - 2x - 5) + 1)) - 1) + 3) + 1) - 2 and g(x) = 3(-4((-1(-3x) - 1)/(2(-3x) + 1)) - 1) - 4 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 5(-1sin(2\u03c0(1|((1(-2|x - 1| + 1) - 3)/(-1(-2|x - 1| + 1) - 2)) - 2| - 1) - 2) + 2) + 3 and g(x) = 1|(-1(-1|(-2e^(-1x) + 2) - 3| - 3)) - 3| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1|(-5(5(3(1x^2 + 2x + 1)) + 4) - 4) - 3| + 1 and g(x) = 3(-2|(5(2|x + 3| - 2) - 3) + 2|) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1((3(2(5((-1x + 3)/(-1x + 2)) - 2)^2 - 4(5((-1x + 3)/(-1x + 2)) - 2) - 4) + 1)/(1(2(5((-1x + 3)/(-1x + 2)) - 2)^2 - 4(5((-1x + 3)/(-1x + 2)) - 2) - 4) + 1)) - 4 and g(x) = 1|(2|(-2e^(-2((-3x + 1)/(-2x - 2))) + 2) - 2| - 1) - 2| - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|(-2((-3(-3|(-4x^2 + 3x - 4) - 3|) + 2)/(-3(-3|(-4x^2 + 3x - 4) - 3|) - 3))^2 - 4((-3(-3|(-4x^2 + 3x - 4) - 3|) + 2)/(-3(-3|(-4x^2 + 3x - 4) - 3|) - 3)) - 3)| - 2 and g(x) = (-1(-4(5((-3x + 2)/(2x + 3)) - 3) - 4) + 3)/(3(-4(5((-3x + 2)/(2x + 3)) - 3) - 4)) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 2((-1(-1(1|(4x - 5) - 3| - 3)^2 + 1(1|(4x - 5) - 3| - 3) - 5))/(-3(-1(1|(4x - 5) - 3| - 3)^2 + 1(1|(4x - 5) - 3| - 3) - 5))) + 2 and g(x) = -1(5(-1e^(1((2x - 2)/(-3x + 2))) + 2)^2 + 2(-1e^(1((2x - 2)/(-3x + 2))) + 2) - 5) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (-2(1(1|(5(2x + 2) + 5) + 2| + 2)^2 - 2(1|(5(2x + 2) + 5) + 2| + 2)) - 3)/(-1(1(1|(5(2x + 2) + 5) + 2| + 2)^2 - 2(1|(5(2x + 2) + 5) + 2| + 2)) + 2) and g(x) = 1|((1(2|((2x - 1)/(-2x)) - 3| - 1))/(-2(2|((2x - 1)/(-2x)) - 3| - 1) + 1)) - 1| + 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3|(2(-1|(-3(5x^2 - 3x - 1) - 3) - 1| + 1) - 3) + 2| and g(x) = 4(-4(1|(-5x^2 + 3x - 1) + 2| - 1)^2 + 3) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2cos(1\u03c0(-1((-1(-3((-2x - 1)/(-2x + 3)) - 1) + 1)/(-2(-3((-2x - 1)/(-2x + 3)) - 1) + 3))^2 + 1((-1(-3((-2x - 1)/(-2x + 3)) - 1) + 1)/(-2(-3((-2x - 1)/(-2x + 3)) - 1) + 3))) + 3) - 3 and g(x) = -2sin(2\u03c0(-2|(2(1|x + 1| + 2) - 2) + 1| + 2) + 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1|(-1(4(1|(-1x - 1) - 1| + 3) + 3)^2 - 3(4(1|(-1x - 1) - 1| + 3) + 3) - 2) - 1| + 1 and g(x) = 5((-2(-3(-1x - 1)^2 + 3(-1x - 1) + 3) - 2)/(-3(-3(-1x - 1)^2 + 3(-1x - 1) + 3))) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1(3(2(1(-4x^2 - 5x + 1) + 4) - 1) - 4) and g(x) = (1(1|((1((3x - 1)/(2x - 1)) - 2)/(-1((3x - 1)/(2x - 1)) + 2)) + 1| - 3) + 2)/(2(1|((1((3x - 1)/(2x - 1)) - 2)/(-1((3x - 1)/(2x - 1)) + 2)) + 1| - 3) + 2) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1(-2|(1e^(-1(-2(4x + 2)^2 + 2(4x + 2) + 1)) + 2) - 2|)^2 + 1(-2|(1e^(-1(-2(4x + 2)^2 + 2(4x + 2) + 1)) + 2) - 2|) and g(x) = 3(-3((-2(4x^2 - 3x - 5) + 1)/(-1(4x^2 - 3x - 5) - 2))) - 4 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3(-3e^(-1((-1(-3((-1x + 3)/(-3x)) - 1) + 1)/(-2(-3((-1x + 3)/(-3x)) - 1) + 1)))) - 1 and g(x) = 1(1sin(2\u03c0((-1(1x^2 + 1x + 4) + 3)/(1(1x^2 + 1x + 4) - 2)) - 2) - 3) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2sin(3\u03c0(-4(3|(1(3|x| + 1)^2 + 5(3|x| + 1) + 3)|)^2 - 3(3|(1(3|x| + 1)^2 + 5(3|x| + 1) + 3)|) + 5) - 2) and g(x) = -5(-2((-2(3cos(1\u03c0x) - 2) + 3)/(-1(3cos(1\u03c0x) - 2))) - 4)^2 - 4(-2((-2(3cos(1\u03c0x) - 2) + 3)/(-1(3cos(1\u03c0x) - 2))) - 4) - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 2e^(1(-3(3(3(-2x^2 + 3x + 4) - 3) - 3) - 2)) - 1 and g(x) = (3(-1sin(2\u03c0(-1|((-2x + 2)/(-2x - 3)) - 1| - 2) - 1) + 1) + 1)/(-3(-1sin(2\u03c0(-1|((-2x + 2)/(-2x - 3)) - 1| - 2) - 1) + 1) + 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -2(3((3(1((-1x - 1)/(-1x + 3)) - 2) + 1)/(3(1((-1x - 1)/(-1x + 3)) - 2) - 2))^2 - 5((3(1((-1x - 1)/(-1x + 3)) - 2) + 1)/(3(1((-1x - 1)/(-1x + 3)) - 2) - 2))) + 2 and g(x) = -1((-1((1(3x - 4))/(2(3x - 4) - 1)) + 2)/(-3((1(3x - 4))/(2(3x - 4) - 1)) - 3)) + 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -1e^(-1(-1(-3((3(3|x - 3| - 2) + 3)/(2(3|x - 3| - 2) - 3)) + 1)^2 + 1(-3((3(3|x - 3| - 2) + 3)/(2(3|x - 3| - 2) - 3)) + 1) + 5)) - 2 and g(x) = 2sin(1\u03c0((2(1|(-1x^2) - 1|) - 2)/(-2(1|(-1x^2) - 1|) + 1)) + 2) - 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -5((-1(4((3((1x + 1)/(-2x + 3)) - 2)/(2((1x + 1)/(-2x + 3)))) - 2) + 1)/(1(4((3((1x + 1)/(-2x + 3)) - 2)/(2((1x + 1)/(-2x + 3)))) - 2) - 3))^2 + 2((-1(4((3((1x + 1)/(-2x + 3)) - 2)/(2((1x + 1)/(-2x + 3)))) - 2) + 1)/(1(4((3((1x + 1)/(-2x + 3)) - 2)/(2((1x + 1)/(-2x + 3)))) - 2) - 3)) + 3 and g(x) = -2e^(1((3(1(-2|x - 1| - 1) + 1) - 3)/(1(1(-2|x - 1| - 1) + 1)))) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -1(1|(1(3|((2x + 3)/(-3x - 1)) + 1| - 3) - 1) + 3| + 1) + 5 and g(x) = 5(5(-1|(-5x^2 + 1x - 5) - 1| - 3) + 3) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 1|((1(3(2(-5x - 1)) - 5) - 2)/(3(3(2(-5x - 1)) - 5) - 2)) - 2| - 3 and g(x) = 2|(2sin(1\u03c0(-2((2x - 1)/(2x - 1))^2 + 5((2x - 1)/(2x - 1)) + 2) - 3) - 1)| - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(-3|(3e^(1(-5(-5x)^2 + 4(-5x) - 1)) - 3) - 2|)^2 - 3(-3|(3e^(1(-5(-5x)^2 + 4(-5x) - 1)) - 3) - 2|) + 2 and g(x) = (-2((-2((-1(-5x^2 + 5x - 3) - 2)/(-3(-5x^2 + 5x - 3) - 3)) + 1)/(-2((-1(-5x^2 + 5x - 3) - 2)/(-3(-5x^2 + 5x - 3) - 3)) - 2)) + 3)/(-3((-2((-1(-5x^2 + 5x - 3) - 2)/(-3(-5x^2 + 5x - 3) - 3)) + 1)/(-2((-1(-5x^2 + 5x - 3) - 2)/(-3(-5x^2 + 5x - 3) - 3)) - 2)) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3(2e^(-2((-1(5(1|x - 3| + 2)) + 3)/(-2(5(1|x - 3| + 2)) - 1))) + 1) + 2 and g(x) = (1(-1(-4((-1x + 1)/(-2x + 1)) + 3)^2 + 1(-4((-1x + 1)/(-2x + 1)) + 3) + 5) - 3)/(-2(-1(-4((-1x + 1)/(-2x + 1)) + 3)^2 + 1(-4((-1x + 1)/(-2x + 1)) + 3) + 5) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1(-2(3(1((2x + 2)/(-2x - 1))^2 + 3((2x + 2)/(-2x - 1)) - 4)^2 - 5(1((2x + 2)/(-2x - 1))^2 + 3((2x + 2)/(-2x - 1)) - 4) + 4)^2 + 2(3(1((2x + 2)/(-2x - 1))^2 + 3((2x + 2)/(-2x - 1)) - 4)^2 - 5(1((2x + 2)/(-2x - 1))^2 + 3((2x + 2)/(-2x - 1)) - 4) + 4) + 5) + 4 and g(x) = 1((3((-1(-1x + 3) + 2)/(-3(-1x + 3) + 2)) + 2)/(1((-1(-1x + 3) + 2)/(-3(-1x + 3) + 2)) - 3)) + 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3((-1(2(-2((1x + 1)/(-3x - 1)) - 2)) - 3)/(-1(2(-2((1x + 1)/(-3x - 1)) - 2)) + 2))^2 - 2((-1(2(-2((1x + 1)/(-3x - 1)) - 2)) - 3)/(-1(2(-2((1x + 1)/(-3x - 1)) - 2)) + 2)) + 2 and g(x) = (-2(-5(-3|(4x - 5) - 1| - 2) - 4) + 2)/(-3(-5(-3|(4x - 5) - 1| - 2) - 4) + 4) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4(-4(-2((1(-4x^2 - 2x - 1) + 2)/(-1(-4x^2 - 2x - 1) - 3)) + 5) - 3) - 5 and g(x) = 2|(2sin(1\u03c0((2((-1x + 2)/(3x + 2)) - 1)/(-3((-1x + 2)/(3x + 2)))) - 3) + 3) + 1| - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1(-4(-1|(-2(-1e^(-2x) - 3)^2 - 1(-1e^(-2x) - 3) - 1) - 1| + 3)^2 + 4(-1|(-2(-1e^(-2x) - 3)^2 - 1(-1e^(-2x) - 3) - 1) - 1| + 3) - 4) - 4 and g(x) = 1(3|(-1|(-5x^2 - 3x + 4) - 1| + 2) + 1|)^2 + 1(3|(-1|(-5x^2 - 3x + 4) - 1| + 2) + 1|) - 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -5(1(-2(5(2x - 3) + 4) - 3) + 1) + 3 and g(x) = (3(1((2(-1x - 2) - 2)/(2(-1x - 2) - 3)) + 5))/(-2(1((2(-1x - 2) - 2)/(2(-1x - 2) - 3)) + 5) - 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 1(-2|(-2(5((-3x)/(-2x + 3))^2 + 5((-3x)/(-2x + 3)) + 2)^2 + 3(5((-3x)/(-2x + 3))^2 + 5((-3x)/(-2x + 3)) + 2)) - 1| - 2)^2 + 5(-2|(-2(5((-3x)/(-2x + 3))^2 + 5((-3x)/(-2x + 3)) + 2)^2 + 3(5((-3x)/(-2x + 3))^2 + 5((-3x)/(-2x + 3)) + 2)) - 1| - 2) - 5 and g(x) = 4(-2|(-1|(4x + 2) - 3| + 2) - 1| - 3)^2 - 3(-2|(-1|(4x + 2) - 3| + 2) - 1| - 3) - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-3(4(1(2sin(3\u03c0(-4x - 1) - 2) + 2)^2 + 5(2sin(3\u03c0(-4x - 1) - 2) + 2) - 2)))/(-1(4(1(2sin(3\u03c0(-4x - 1) - 2) + 2)^2 + 5(2sin(3\u03c0(-4x - 1) - 2) + 2) - 2)) + 2) and g(x) = 2(2((-1(-3x^2 - 3x - 3) - 2)/(1(-3x^2 - 3x - 3)))^2 - 4((-1(-3x^2 - 3x - 3) - 2)/(1(-3x^2 - 3x - 3))) + 5)^2 - 3(2((-1(-3x^2 - 3x - 3) - 2)/(1(-3x^2 - 3x - 3)))^2 - 4((-1(-3x^2 - 3x - 3) - 2)/(1(-3x^2 - 3x - 3))) + 5) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 3(-1e^(2(3(-3|(5x - 1) + 3| + 2) - 2)) + 1) + 3 and g(x) = -1(1(1sin(1\u03c0(-5x^2 + 2x + 4) - 1) - 2)^2 + 4(1sin(1\u03c0(-5x^2 + 2x + 4) - 1) - 2) - 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-3(2((-2(1(1x - 5) + 4) + 3)/(-1(1(1x - 5) + 4) - 2)) + 4) + 1)/(-2(2((-2(1(1x - 5) + 4) + 3)/(-1(1(1x - 5) + 4) - 2)) + 4) + 3) and g(x) = (-1(-4((2(5x + 3) - 2)/(1(5x + 3) + 3))^2))/(3(-4((2(5x + 3) - 2)/(1(5x + 3) + 3))^2) - 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 3|(-2(3|((2(-3x + 4) + 1)/(-3(-3x + 4) + 1)) - 2| - 2)^2 - 3(3|((2(-3x + 4) + 1)/(-3(-3x + 4) + 1)) - 2| - 2) + 5) - 2| + 3 and g(x) = 3|(2(-5(5x - 5)^2 - 4(5x - 5) + 3)^2 + 4(-5(5x - 5)^2 - 4(5x - 5) + 3) - 1) + 3| - 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1|(1sin(1\u03c0(3|(2|(2x + 5) + 1|) - 3| - 3) + 1) + 1)| and g(x) = 3((2(-5(3x) + 1) - 2)/(-1(-5(3x) + 1) - 2)) - 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (3(-4(-4(1|(-1|x - 2| - 3) - 1| - 2) - 2)^2 + 3(-4(1|(-1|x - 2| - 3) - 1| - 2) - 2) + 5) - 1)/(-3(-4(-4(1|(-1|x - 2| - 3) - 1| - 2) - 2)^2 + 3(-4(1|(-1|x - 2| - 3) - 1| - 2) - 2) + 5) + 2) and g(x) = (-2(-1|(-4((-3x + 3)/(2x + 2))^2 - 4((-3x + 3)/(2x + 2))) + 3| - 2) - 3)/(1(-1|(-4((-3x + 3)/(2x + 2))^2 - 4((-3x + 3)/(2x + 2))) + 3| - 2) - 2) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 3(-2sin(3\u03c0(-2|(5(1x^2 + 5x - 3)^2 - 4(1x^2 + 5x - 3) + 4) - 1| + 1) + 1) - 2)^2 - 3(-2sin(3\u03c0(-2|(5(1x^2 + 5x - 3)^2 - 4(1x^2 + 5x - 3) + 4) - 1| + 1) + 1) - 2) + 4 and g(x) = -3(-2cos(1\u03c0(-2(2|x + 2| + 2)^2 + 5(2|x + 2| + 2) - 5) + 3) - 1) - 5 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (1(5(1(-5(4x^2 - 2x - 4)^2 - 3(4x^2 - 2x - 4) + 3) - 2) + 3) - 2)/(-3(5(1(-5(4x^2 - 2x - 4)^2 - 3(4x^2 - 2x - 4) + 3) - 2) + 3) + 2) and g(x) = (-2(-2|(2(-1|x - 3| - 3)^2 + 3(-1|x - 3| - 3) - 3) + 3| - 2) + 2)/(1(-2|(2(-1|x - 3| - 3)^2 + 3(-1|x - 3| - 3) - 3) + 3| - 2) + 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1(5((-1(-1cos(3\u03c0((2x)/(-1x - 1)) + 1) - 3))/(2(-1cos(3\u03c0((2x)/(-1x - 1)) + 1) - 3)))^2 - 2((-1(-1cos(3\u03c0((2x)/(-1x - 1)) + 1) - 3))/(2(-1cos(3\u03c0((2x)/(-1x - 1)) + 1) - 3))) - 3)^2 + 1(5((-1(-1cos(3\u03c0((2x)/(-1x - 1)) + 1) - 3))/(2(-1cos(3\u03c0((2x)/(-1x - 1)) + 1) - 3)))^2 - 2((-1(-1cos(3\u03c0((2x)/(-1x - 1)) + 1) - 3))/(2(-1cos(3\u03c0((2x)/(-1x - 1)) + 1) - 3))) - 3) - 4 and g(x) = -1|(-1|(1(-3x^2 - 5x + 2) + 1) - 1| + 1) + 1| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the third intersection point (counting from left to right) between the functions f(x) = -3cos(1\u03c0(-1(1|(-1(4x + 1)^2 + 1(4x + 1) - 4) - 3| - 3)^2 - 3(1|(-1(4x + 1)^2 + 1(4x + 1) - 4) - 3| - 3) - 4) + 2) - 3 and g(x) = -4(-2(4((-3x + 3)/(-2x + 1)) + 2) - 2)^2 + 1(-2(4((-3x + 3)/(-2x + 1)) + 2) - 2) + 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3((3(4((-1((1x - 1)/(-2x + 3)) - 1)/(3((1x - 1)/(-2x + 3)) - 2)) - 1) + 2)/(2(4((-1((1x - 1)/(-2x + 3)) - 1)/(3((1x - 1)/(-2x + 3)) - 2)) - 1) + 2)) - 4 and g(x) = 1((2(-2((-2x + 1)/(-1x + 3))^2 - 3((-2x + 1)/(-1x + 3)) + 2) + 2)/(-1(-2((-2x + 1)/(-1x + 3))^2 - 3((-2x + 1)/(-1x + 3)) + 2) + 2))^2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1(3(-4((-3(-2e^(1x) - 3) + 2)/(2(-2e^(1x) - 3) - 3)) - 2)^2 + 4(-4((-3(-2e^(1x) - 3) + 2)/(2(-2e^(1x) - 3) - 3)) - 2)) + 5 and g(x) = -1|(-1|(5(-1x) + 1) - 1|)| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|((1(-4((1((-2x + 3)/(1x + 2)) - 1)/(-3((-2x + 3)/(1x + 2)) - 1)) - 4) + 3)/(2(-4((1((-2x + 3)/(1x + 2)) - 1)/(-3((-2x + 3)/(1x + 2)) - 1)) - 4)))| - 3 and g(x) = 1((-2((-3(5x^2 - 1x - 3) - 2)/(-3(5x^2 - 1x - 3) - 3)) - 1)/(2((-3(5x^2 - 1x - 3) - 2)/(-3(5x^2 - 1x - 3) - 3)) - 3))^2 - 5((-2((-3(5x^2 - 1x - 3) - 2)/(-3(5x^2 - 1x - 3) - 3)) - 1)/(2((-3(5x^2 - 1x - 3) - 2)/(-3(5x^2 - 1x - 3) - 3)) - 3)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-3(-4(-1cos(3\u03c0(-1(-2x^2 - 3x - 2) + 5) + 1) - 3) + 2) + 1)/(-3(-4(-1cos(3\u03c0(-1(-2x^2 - 3x - 2) + 5) + 1) - 3) + 2) + 4) and g(x) = 1(-5(1e^(1((-1x)/(3x - 2))) - 3) + 4)^2 - 2(-5(1e^(1((-1x)/(3x - 2))) - 3) + 4) - 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(-2|(2e^(1(3|(-5x^2 - 5x) - 2| + 2))) - 3| + 2) + 1)/(2(-2|(2e^(1(3|(-5x^2 - 5x) - 2| + 2))) - 3| + 2) + 1) and g(x) = (2(-4((2((-3x)/(-2x - 3)) + 3)/(2((-3x)/(-2x - 3)) + 2))) - 1)/(-1(-4((2((-3x)/(-2x - 3)) + 3)/(2((-3x)/(-2x - 3)) + 2))) + 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1cos(2\u03c0((-1(-4((3(3|x - 3| + 1) + 2)/(2(3|x - 3| + 1) - 1)) - 5) - 2)/(-3(-4((3(3|x - 3| + 1) + 2)/(2(3|x - 3| + 1) - 1)) - 5) + 1)) - 2) + 1 and g(x) = 2(-4(1e^(-1((1x + 2)/(-3x + 2))) - 1)^2 - 2(1e^(-1((1x + 2)/(-3x + 2))) - 1) + 4) - 1 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (3(-1(-1|((-1(-4x) + 3)/(3(-4x) + 3))| + 3) + 5) + 3)/(-3(-1(-1|((-1(-4x) + 3)/(3(-4x) + 3))| + 3) + 5) + 2) and g(x) = (-2(-5((3(-2e^(-1x) + 1) - 3)/(1(-2e^(-1x) + 1) + 2))^2 + 3((3(-2e^(-1x) + 1) - 3)/(1(-2e^(-1x) + 1) + 2)) - 3) + 1)/(2(-5((3(-2e^(-1x) + 1) - 3)/(1(-2e^(-1x) + 1) + 2))^2 + 3((3(-2e^(-1x) + 1) - 3)/(1(-2e^(-1x) + 1) + 2)) - 3) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(-4(-3|(-2|(-2|x + 1| - 1) - 2| - 2) + 2| + 2) + 4) - 3| - 2 and g(x) = (3(1(3(-1x^2 - 2x) - 4) + 2) + 1)/(-1(1(3(-1x^2 - 2x) - 4) + 2) - 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1((-3(-5(2sin(3\u03c0((-1x)/(-2x + 3)) - 1) + 3) - 5) - 2)/(3(-5(2sin(3\u03c0((-1x)/(-2x + 3)) - 1) + 3) - 5) - 1)) - 2 and g(x) = (1((3((1((3x)/(-1x - 3)))/(1((3x)/(-1x - 3)) - 2)) - 2)/(1((1((3x)/(-1x - 3)))/(1((3x)/(-1x - 3)) - 2)) + 2)) + 3)/(-2((3((1((3x)/(-1x - 3)))/(1((3x)/(-1x - 3)) - 2)) - 2)/(1((1((3x)/(-1x - 3)))/(1((3x)/(-1x - 3)) - 2)) + 2))) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (3(-2(-5(-5(-4x^2 + 1x + 1) + 3) - 1)^2 + 4(-5(-5(-4x^2 + 1x + 1) + 3) - 1)) + 3)/(-1(-2(-5(-5(-4x^2 + 1x + 1) + 3) - 1)^2 + 4(-5(-5(-4x^2 + 1x + 1) + 3) - 1))) and g(x) = (1(-2e^(-1(2((-3x - 3)/(-3x + 2))^2 - 1((-3x - 3)/(-3x + 2)) + 3)) - 3) - 3)/(2(-2e^(-1(2((-3x - 3)/(-3x + 2))^2 - 1((-3x - 3)/(-3x + 2)) + 3)) - 3) + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (3((-1(1(1(-3|x - 3| - 3))^2 + 5(1(-3|x - 3| - 3)) + 3) + 3)/(-3(1(1(-3|x - 3| - 3))^2 + 5(1(-3|x - 3| - 3)) + 3) - 1)) - 2)/(-1((-1(1(1(-3|x - 3| - 3))^2 + 5(1(-3|x - 3| - 3)) + 3) + 3)/(-3(1(1(-3|x - 3| - 3))^2 + 5(1(-3|x - 3| - 3)) + 3) - 1)) - 1) and g(x) = -2|(2cos(3\u03c0((-2(1x^2 + 5x + 4))/(-3(1x^2 + 5x + 4) - 2)) + 3) - 2) + 1| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -1(2e^(-1((3(1|(1x^2 - 2x - 4) - 2|))/(-1(1|(1x^2 - 2x - 4) - 2|) - 2))) - 2)^2 - 1(2e^(-1((3(1|(1x^2 - 2x - 4) - 2|))/(-1(1|(1x^2 - 2x - 4) - 2|) - 2))) - 2) + 1 and g(x) = 1|((3(3((1x)/(3x + 3)) - 2) - 2)/(-1(3((1x)/(3x + 3)) - 2) - 1))| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -1((1(2|((-3(4x - 3))/(2(4x - 3) - 1)) + 1|) - 3)/(-2(2|((-3(4x - 3))/(2(4x - 3) - 1)) + 1|) + 3)) - 2 and g(x) = -1|(-1|(2(2x - 5) + 3) + 2| + 2) + 2| - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2(-1|(1(-2e^(-1((3x - 3)/(-2x - 3))) + 3)^2 + 5(-2e^(-1((3x - 3)/(-2x - 3))) + 3) + 5) - 3| + 3) + 2)/(2(-1|(1(-2e^(-1((3x - 3)/(-2x - 3))) + 3)^2 + 5(-2e^(-1((3x - 3)/(-2x - 3))) + 3) + 5) - 3| + 3) + 3) and g(x) = (2(-1sin(1\u03c0(2((1x - 1)/(2x)) - 2)) + 1))/(3(-1sin(1\u03c0(2((1x - 1)/(2x)) - 2)) + 1) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = (-1(1|(4(-3(4x - 4)^2 - 2(4x - 4) + 3)^2 - 1(-3(4x - 4)^2 - 2(4x - 4) + 3) + 3) - 2| - 3) - 3)/(-2(1|(4(-3(4x - 4)^2 - 2(4x - 4) + 3)^2 - 1(-3(4x - 4)^2 - 2(4x - 4) + 3) + 3) - 2| - 3) - 3) and g(x) = 2cos(3\u03c0((1(5(-5x^2 + 5x - 4)) + 2)/(-2(5(-5x^2 + 5x - 4)) - 1)) - 1) - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (2(2|(2|(1(-3cos(3\u03c0x - 2) + 3) + 4) - 3| - 1) + 2| + 2) - 2)/(-1(2|(2|(1(-3cos(3\u03c0x - 2) + 3) + 4) - 3| - 1) + 2| + 2) - 3) and g(x) = -4((-1(-1((3x - 1)/(-1x - 1)) - 5) - 2)/(2(-1((3x - 1)/(-1x - 1)) - 5) - 1)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2(3|(1(2|(5x - 1) - 1| - 1)) - 2| - 3) and g(x) = 4(4(4((-1x + 1)/(3x - 2))^2 - 4((-1x + 1)/(3x - 2)) - 4) + 4) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-2((-1(5(2|((3x + 2)/(3x + 1)) + 2| - 1)^2 + 4(2|((3x + 2)/(3x + 1)) + 2| - 1) + 3) - 3)/(3(5(2|((3x + 2)/(3x + 1)) + 2| - 1)^2 + 4(2|((3x + 2)/(3x + 1)) + 2| - 1) + 3) - 2)))/(-3((-1(5(2|((3x + 2)/(3x + 1)) + 2| - 1)^2 + 4(2|((3x + 2)/(3x + 1)) + 2| - 1) + 3) - 3)/(3(5(2|((3x + 2)/(3x + 1)) + 2| - 1)^2 + 4(2|((3x + 2)/(3x + 1)) + 2| - 1) + 3) - 2)) - 1) and g(x) = 1(3|(-3((-2x - 3)/(2x - 1))^2 + 3((-2x - 3)/(2x - 1)) + 1) - 2| + 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2(-1|(-2cos(2\u03c0((3(-1|x| + 2) + 3)/(-2(-1|x| + 2) - 2)) - 2) + 3) + 3| + 2)^2 + 3(-1|(-2cos(2\u03c0((3(-1|x| + 2) + 3)/(-2(-1|x| + 2) - 2)) - 2) + 3) + 3| + 2) + 2 and g(x) = -2(-1|((-1((1x + 3)/(-1x - 1)) - 1)/(1((1x + 3)/(-1x - 1)))) + 1| - 1) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 5((-2((-1(3(2x + 5)^2 - 5(2x + 5) + 4) - 1)/(1(3(2x + 5)^2 - 5(2x + 5) + 4) - 3)) - 2)/(-2((-1(3(2x + 5)^2 - 5(2x + 5) + 4) - 1)/(1(3(2x + 5)^2 - 5(2x + 5) + 4) - 3)) - 3)) + 4 and g(x) = 2((-1((1(-3e^(-1x) + 3))/(1(-3e^(-1x) + 3) + 1)) - 3)/(3((1(-3e^(-1x) + 3))/(1(-3e^(-1x) + 3) + 1)) + 1)) - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1|(1(-2(2((1x - 2)/(2x + 3))^2 - 3)^2 - 3(2((1x - 2)/(2x + 3))^2 - 3) + 5)^2 - 1(-2(2((1x - 2)/(2x + 3))^2 - 3)^2 - 3(2((1x - 2)/(2x + 3))^2 - 3) + 5) + 2) - 3| and g(x) = (-1(4(-5(4x - 1))^2 - 4(-5(4x - 1)) - 1) - 1)/(-3(4(-5(4x - 1))^2 - 4(-5(4x - 1)) - 1) + 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -5(1cos(2\u03c0(2(-1|(-2|x - 1| + 3)| - 1)) + 2) + 3)^2 - 1(1cos(2\u03c0(2(-1|(-2|x - 1| + 3)| - 1)) + 2) + 3) - 2 and g(x) = (2(1(-2cos(2\u03c0(-2|x + 2| + 3) - 2) - 2)^2 - 3(-2cos(2\u03c0(-2|x + 2| + 3) - 2) - 2) - 2) - 3)/(2(1(-2cos(2\u03c0(-2|x + 2| + 3) - 2) - 2)^2 - 3(-2cos(2\u03c0(-2|x + 2| + 3) - 2) - 2) - 2) - 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -1(-2|((2(-3|((2x + 3)/(2x + 2)) - 1|) + 3)/(-2(-3|((2x + 3)/(2x + 2)) - 1|) - 2)) - 2| - 3)^2 + 4(-2|((2(-3|((2x + 3)/(2x + 2)) - 1|) + 3)/(-2(-3|((2x + 3)/(2x + 2)) - 1|) - 2)) - 2| - 3) + 4 and g(x) = -2(4((2((1x + 3)/(2x - 1)) + 2)/(3((1x + 3)/(2x - 1)) - 2))^2 + 1((2((1x + 3)/(2x - 1)) + 2)/(3((1x + 3)/(2x - 1)) - 2)) - 4)^2 - 4(4((2((1x + 3)/(2x - 1)) + 2)/(3((1x + 3)/(2x - 1)) - 2))^2 + 1((2((1x + 3)/(2x - 1)) + 2)/(3((1x + 3)/(2x - 1)) - 2)) - 4) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 2|(-4(1|((1(-1x - 1) - 3)/(-1(-1x - 1) - 3)) - 1| - 3)^2 + 2(1|((1(-1x - 1) - 3)/(-1(-1x - 1) - 3)) - 1| - 3) + 3) + 2| + 3 and g(x) = (-3(-1e^(2((1(-3x^2 - 4x + 5) - 2)/(3(-3x^2 - 4x + 5) - 2)))))/(-3(-1e^(2((1(-3x^2 - 4x + 5) - 2)/(3(-3x^2 - 4x + 5) - 2)))) - 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|(-4(3sin(2\u03c0((3(-3|x + 3| - 3) - 2)/(3(-3|x + 3| - 3) - 1)) + 2) + 1)^2 + 2(3sin(2\u03c0((3(-3|x + 3| - 3) - 2)/(3(-3|x + 3| - 3) - 1)) + 2) + 1) - 1) + 1| + 1 and g(x) = (-2(-1(-2(-2x + 1)^2 - 1(-2x + 1) + 4) - 3) + 3)/(3(-1(-2(-2x + 1)^2 - 1(-2x + 1) + 4) - 3) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(2(4((2(-1x^2 - 3x - 4) - 3)/(-1(-1x^2 - 3x - 4))) + 4)^2 - 3(4((2(-1x^2 - 3x - 4) - 3)/(-1(-1x^2 - 3x - 4))) + 4) + 5) - 2)/(1(2(4((2(-1x^2 - 3x - 4) - 3)/(-1(-1x^2 - 3x - 4))) + 4)^2 - 3(4((2(-1x^2 - 3x - 4) - 3)/(-1(-1x^2 - 3x - 4))) + 4) + 5)) and g(x) = 5((2(-2|((1x + 3)/(-3x - 1)) - 1| + 3) + 2)/(2(-2|((1x + 3)/(-3x - 1)) - 1| + 3) + 1)) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3(3(-5(-5(-4x^2 + 2x + 3)^2 + 5(-4x^2 + 2x + 3) - 3)^2 + 4(-5(-4x^2 + 2x + 3)^2 + 5(-4x^2 + 2x + 3) - 3) - 2) - 1) + 4 and g(x) = -1|(-3(2|(3|x - 1| - 1) + 2|)^2 + 2(2|(3|x - 1| - 1) + 2|) + 5) + 2| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 5(2(-1(-3|(-4x^2 + 1x - 1) - 1| + 3)^2 - 5(-3|(-4x^2 + 1x - 1) - 1| + 3) + 3) + 5) - 1 and g(x) = 3cos(1\u03c0((-1(-1|(1|x + 2| + 2) + 1|) - 3)/(2(-1|(1|x + 2| + 2) + 1|) - 1)) + 3) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4(4(5(1(4x^2 - 5x - 4)^2 + 3(4x^2 - 5x - 4))^2 - 3(1(4x^2 - 5x - 4)^2 + 3(4x^2 - 5x - 4)) + 4) + 5) + 4 and g(x) = -4(-3(2(5x + 3)^2 + 5(5x + 3) + 3)^2 - 2(2(5x + 3)^2 + 5(5x + 3) + 3) - 5)^2 + 2(-3(2(5x + 3)^2 + 5(5x + 3) + 3)^2 - 2(2(5x + 3)^2 + 5(5x + 3) + 3) - 5) - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(2|(4(-3(2x - 3)^2 + 1) + 4) - 2| - 2) + 3)/(3(2|(4(-3(2x - 3)^2 + 1) + 4) - 2| - 2) + 1) and g(x) = -4(4(5(2x + 3))^2 - 5(5(2x + 3)) - 5) - 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3|(-5(-1e^(-1(-3|(2x - 4) - 2|)) - 1) - 5) - 1| - 2 and g(x) = -2|(-2|(-2(-1|x + 2|)^2 - 2(-1|x + 2|) - 1) + 2| + 1) + 3| + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1|(-2|(3(2|(-5x - 3) - 3| - 1) + 4) + 1| + 3) + 1| + 3 and g(x) = 3(2(-1(-3x + 2) - 5) + 4)^2 - 4(2(-1(-3x + 2) - 5) + 4) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -3(1(5(-5(-4x + 1) + 2)^2 - 2(-5(-4x + 1) + 2) - 3) - 4) - 4 and g(x) = -3|(5(4(2e^(-1x) - 2)^2 - 5(2e^(-1x) - 2) - 1) - 1) + 2| + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 5(-1(2|(3((-2x - 1)/(2x - 1)) - 2)| + 1)^2 - 1(2|(3((-2x - 1)/(2x - 1)) - 2)| + 1) - 2)^2 - 4(-1(2|(3((-2x - 1)/(2x - 1)) - 2)| + 1)^2 - 1(2|(3((-2x - 1)/(2x - 1)) - 2)| + 1) - 2) and g(x) = 3|(-5((3((-1x + 2)/(1x - 3)) + 3)/(2((-1x + 2)/(1x - 3)) - 3))^2 - 2((3((-1x + 2)/(1x - 3)) + 3)/(2((-1x + 2)/(1x - 3)) - 3)) + 1) + 2| - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3(-2(3e^(-2(2|(1|x + 2| + 1) - 2| - 1)))^2 - 5)^2 + 1(-2(3e^(-2(2|(1|x + 2| + 1) - 2| - 1)))^2 - 5) - 1 and g(x) = 3((-1((2((1x + 1)/(-2x + 3)) - 2)/(-1((1x + 1)/(-2x + 3)) - 3)) - 2)/(2((2((1x + 1)/(-2x + 3)) - 2)/(-1((1x + 1)/(-2x + 3)) - 3)) - 3)) - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 2|(-1(4(5(-1x - 2) + 4)^2 - 3)^2 - 4(4(5(-1x - 2) + 4)^2 - 3) + 3) - 3| - 2 and g(x) = -1(-4((-2((-3x + 1)/(-3x + 4)) - 3)/(-1((-3x + 1)/(-3x + 4)))) + 3) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (3(-5((-2((1(-5x + 5) - 2)/(1(-5x + 5) + 2)) - 1)/(2((1(-5x + 5) - 2)/(1(-5x + 5) + 2))))^2 + 4((-2((1(-5x + 5) - 2)/(1(-5x + 5) + 2)) - 1)/(2((1(-5x + 5) - 2)/(1(-5x + 5) + 2)))) - 4) - 1)/(2(-5((-2((1(-5x + 5) - 2)/(1(-5x + 5) + 2)) - 1)/(2((1(-5x + 5) - 2)/(1(-5x + 5) + 2))))^2 + 4((-2((1(-5x + 5) - 2)/(1(-5x + 5) + 2)) - 1)/(2((1(-5x + 5) - 2)/(1(-5x + 5) + 2)))) - 4) - 1) and g(x) = (-1(3(2|(-4x - 1) - 2| - 3) - 5) - 3)/(1(3(2|(-4x - 1) - 2| - 3) - 5)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1((-3(1e^(1((1(-3x^2 + 1x + 4) - 3)/(2(-3x^2 + 1x + 4) + 2))) + 1) - 3)/(1(1e^(1((1(-3x^2 + 1x + 4) - 3)/(2(-3x^2 + 1x + 4) + 2))) + 1) - 2)) + 2 and g(x) = 2(-4(2(-5x + 2)^2 + 3(-5x + 2) - 4)^2 - 4(2(-5x + 2)^2 + 3(-5x + 2) - 4) - 5) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (2((1(2|(1|(-1e^(2x) - 2) - 2| - 3)| + 3) - 2)/(1(2|(1|(-1e^(2x) - 2) - 2| - 3)| + 3))) + 3)/(-1((1(2|(1|(-1e^(2x) - 2) - 2| - 3)| + 3) - 2)/(1(2|(1|(-1e^(2x) - 2) - 2| - 3)| + 3))) + 2) and g(x) = (2(3|(-2|((3x)/(1x - 2))| + 2) + 3| + 1) - 2)/(-1(3|(-2|((3x)/(1x - 2))| + 2) + 3| + 1) + 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 2|(-1((2((-1(-3|x - 2|) + 2)/(3(-3|x - 2|) - 2)))/(-1((-1(-3|x - 2|) + 2)/(3(-3|x - 2|) - 2)))) + 2) - 3| + 1 and g(x) = 3e^(-2(1|((-2(3|x| - 1) - 3)/(3(3|x| - 1) - 2)) + 3| - 3)) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 2cos(1\u03c0(-1(-3(5(2x + 3) + 2) - 5)^2 - 4(-3(5(2x + 3) + 2) - 5) + 5) + 2) - 3 and g(x) = (-1(-4(3(-2x + 1) + 4) + 5) - 3)/(3(-4(3(-2x + 1) + 4) + 5)) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -2(2|((-3(1|(3x^2 + 3x + 5) - 2| + 1) - 2)/(3(1|(3x^2 + 3x + 5) - 2| + 1) + 3))| + 1) - 3 and g(x) = -1(-4((3(3x + 2) - 3)/(-3(3x + 2) + 4)) + 5)^2 + 1(-4((3(3x + 2) - 3)/(-3(3x + 2) + 4)) + 5) - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2(-2(-1|((3((2x)/(3x + 1)) + 2)/(-2((2x)/(3x + 1)) - 2)) - 1|)^2 + 3)^2 - 2(-2(-1|((3((2x)/(3x + 1)) + 2)/(-2((2x)/(3x + 1)) - 2)) - 1|)^2 + 3) - 5 and g(x) = -3|(-2sin(2\u03c0((-3((1x + 3)/(-2x - 2)) + 2)/(-1((1x + 3)/(-2x - 2)))) - 2) + 3) - 3| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -2|(1|(-3|(-5(-1sin(2\u03c0x + 1) - 3) + 2) + 2| - 1) + 3| - 3) - 3| - 3 and g(x) = -1|(-2|(1e^(-1(2x - 1))) + 1| - 3) - 3| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -2|(2|(3|(-3e^(-2(3|x + 2| - 2)) + 3) - 3| + 1) + 1| + 2) - 3| + 3 and g(x) = -3(1e^(1((1((2x - 2)/(-3x + 2)) - 1)/(-3((2x - 2)/(-3x + 2)) + 4))))^2 - 4(1e^(1((1((2x - 2)/(-3x + 2)) - 1)/(-3((2x - 2)/(-3x + 2)) + 4)))) + 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (1(-2e^(2((2(-1(2|x| - 3) - 3) + 1)/(1(-1(2|x| - 3) - 3) + 2))) - 2) + 2)/(-3(-2e^(2((2(-1(2|x| - 3) - 3) + 1)/(1(-1(2|x| - 3) - 3) + 2))) - 2) + 4) and g(x) = -2e^(-1(-1(3|(3x + 3) + 3| - 3) - 1)) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-3((2(1|(2((3x - 2)/(2x)) - 1)| - 2) + 1)/(2(1|(2((3x - 2)/(2x)) - 1)| - 2) + 1)) - 3)/(-1((2(1|(2((3x - 2)/(2x)) - 1)| - 2) + 1)/(2(1|(2((3x - 2)/(2x)) - 1)| - 2) + 1)) + 2) and g(x) = -1e^(1((2((-1(1x - 2) - 2)/(-2(1x - 2) + 1)) + 3)/(-1((-1(1x - 2) - 2)/(-2(1x - 2) + 1)) - 1))) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2e^(2((1(4(-2(2x - 5)^2 - 1(2x - 5) - 2)^2 - 5(-2(2x - 5)^2 - 1(2x - 5) - 2) - 2) + 3)/(-2(4(-2(2x - 5)^2 - 1(2x - 5) - 2)^2 - 5(-2(2x - 5)^2 - 1(2x - 5) - 2) - 2) + 1))) and g(x) = -2((2(-3e^(-1((3x + 1)/(1x + 3))) + 2) - 1)/(1(-3e^(-1((3x + 1)/(1x + 3))) + 2)))^2 + 2((2(-3e^(-1((3x + 1)/(1x + 3))) + 2) - 1)/(1(-3e^(-1((3x + 1)/(1x + 3))) + 2))) - 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -2|(-3|(1cos(3\u03c0(2|(-2x^2 + 3x + 3) - 3| - 3) + 1) + 1) - 3|) + 3| - 1 and g(x) = (2(-2((1(-3|x - 1| + 2) + 1)/(2(-3|x - 1| + 2))) - 2) + 3)/(3(-2((1(-3|x - 1| + 2) + 1)/(2(-3|x - 1| + 2))) - 2) + 3) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1(2e^(-1(1((1(-2x) + 3)/(2(-2x))) + 1)) + 3)^2 + 5(2e^(-1(1((1(-2x) + 3)/(2(-2x))) + 1)) + 3) + 4 and g(x) = -5((-2(1e^(-2((3x)/(3x - 1))) + 1) - 3)/(2(1e^(-2((3x)/(3x - 1))) + 1) + 3)) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 1(1(3(3(5x - 3)^2 - 2(5x - 3))^2 - 1(3(5x - 3)^2 - 2(5x - 3)) + 1) - 2)^2 - 4(1(3(3(5x - 3)^2 - 2(5x - 3))^2 - 1(3(5x - 3)^2 - 2(5x - 3)) + 1) - 2) + 2 and g(x) = -3(-1|(2sin(2\u03c0(-1x + 4) - 1) - 2) + 2| - 1)^2 - 4(-1|(2sin(2\u03c0(-1x + 4) - 1) - 2) + 2| - 1) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-4(2((-2(-2x) - 2)/(-1(-2x) + 3)) + 5)^2 + 1(2((-2(-2x) - 2)/(-1(-2x) + 3)) + 5) + 5) + 1 and g(x) = -2e^(-1((1(-3|(3x^2 + 3x) - 1| + 2) + 3)/(2(-3|(3x^2 + 3x) - 1| + 2)))) - 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|(5((-3(-3e^(-2((2x + 1)/(-1x + 3))) - 1) + 3)/(3(-3e^(-2((2x + 1)/(-1x + 3))) - 1) - 2))^2 - 1((-3(-3e^(-2((2x + 1)/(-1x + 3))) - 1) + 3)/(3(-3e^(-2((2x + 1)/(-1x + 3))) - 1) - 2)) - 1) - 1| + 3 and g(x) = 1(-4(-3((-1x + 3)/(-2x - 3)) + 5) - 1) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -1(5(1((1(-1x - 3) + 1)/(1(-1x - 3) + 2)) - 1) - 3) + 2 and g(x) = (2(2|(-3(4x^2) - 3) - 1| + 1) + 2)/(2(2|(-3(4x^2) - 3) - 1| + 1) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (1(-3(2(-1((-2x)/(2x + 2)) - 1) + 2) + 3) - 1)/(-3(-3(2(-1((-2x)/(2x + 2)) - 1) + 2) + 3) - 1) and g(x) = -5(1(-4(4x - 4)^2 + 3(4x - 4) - 4) + 3) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (2(1(1e^(1(-4(-3x^2 + 3x - 1)^2 + 4)) + 1) - 2) + 3)/(2(1(1e^(1(-4(-3x^2 + 3x - 1)^2 + 4)) + 1) - 2) + 1) and g(x) = -3|(2((-2(1|x| - 1))/(-1(1|x| - 1) - 2)) + 1)| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 1(5(-1(-1(2x^2 - 1x - 3) + 3) + 3) + 5) - 1 and g(x) = -3(-2(-1sin(1\u03c0((3x + 1)/(2x - 1)) - 3)) - 2) - 1 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 3((2((2(2|(3x^2 + 5x - 3)| + 3) + 1)/(-2(2|(3x^2 + 5x - 3)| + 3) + 3)) - 1)/(-3((2(2|(3x^2 + 5x - 3)| + 3) + 1)/(-2(2|(3x^2 + 5x - 3)| + 3) + 3)))) - 1 and g(x) = (1(-2((1(5x - 1) - 3)/(2(5x - 1) + 1))^2 - 4((1(5x - 1) - 3)/(2(5x - 1) + 1)) - 1))/(3(-2((1(5x - 1) - 3)/(2(5x - 1) + 1))^2 - 4((1(5x - 1) - 3)/(2(5x - 1) + 1)) - 1) - 2) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -2((-3(-3e^(-2((1((1x - 2)/(2x + 1)) + 1)/(-2((1x - 2)/(2x + 1))))) - 3) - 2)/(-1(-3e^(-2((1((1x - 2)/(2x + 1)) + 1)/(-2((1x - 2)/(2x + 1))))) - 3) - 1))^2 + 2((-3(-3e^(-2((1((1x - 2)/(2x + 1)) + 1)/(-2((1x - 2)/(2x + 1))))) - 3) - 2)/(-1(-3e^(-2((1((1x - 2)/(2x + 1)) + 1)/(-2((1x - 2)/(2x + 1))))) - 3) - 1)) - 4 and g(x) = 5(-1(-5(1x - 5)^2 - 5(1x - 5) - 3) - 5) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 2|((-2(-2(-3|(3x + 4) - 3| - 2) - 4) + 2)/(3(-2(-3|(3x + 4) - 3| - 2) - 4) - 2)) - 3| + 2 and g(x) = (-1((-1(-1e^(-1((1x + 3)/(3x + 1))) + 2))/(2(-1e^(-1((1x + 3)/(3x + 1))) + 2) - 3)) - 1)/(1((-1(-1e^(-1((1x + 3)/(3x + 1))) + 2))/(2(-1e^(-1((1x + 3)/(3x + 1))) + 2) - 3)) + 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-1((-3(4(3(-3x)) - 4) + 1)/(-2(4(3(-3x)) - 4) + 3)) - 3)/(3((-3(4(3(-3x)) - 4) + 1)/(-2(4(3(-3x)) - 4) + 3)) + 2) and g(x) = 3(-2|((2((-3x + 1)/(3x)) - 3)/(2((-3x + 1)/(3x)) + 2)) - 3| + 1) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 2|(5(-3|((-1(2|x + 3| + 3) + 1)/(2(2|x + 3| + 3) + 3)) - 1| + 3) + 3) + 1| + 2 and g(x) = 2|(4((2(3x^2 + 3x + 2) - 1)/(1(3x^2 + 3x + 2)))) - 3| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-1((3(-3|(-4(2|x| + 3) - 4) + 1| + 3) + 3)/(-1(-3|(-4(2|x| + 3) - 4) + 1| + 3) + 2)))/(-3((3(-3|(-4(2|x| + 3) - 4) + 1| + 3) + 3)/(-1(-3|(-4(2|x| + 3) - 4) + 1| + 3) + 2)) + 4) and g(x) = 2e^(1(4((3((1x - 2)/(2x + 1)) + 3)/(-2((1x - 2)/(2x + 1)))) - 1)) - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1(-1|((1(5(1sin(2\u03c0x + 1) + 1) + 2) - 3)/(1(5(1sin(2\u03c0x + 1) + 1) + 2))) - 3| + 2) + 2 and g(x) = -3(-5(4(2x + 5)^2 - 4(2x + 5)) - 2) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-2(-2(4(2cos(2\u03c0(1x - 1) + 2) + 2) - 1) - 5) + 1)/(3(-2(4(2cos(2\u03c0(1x - 1) + 2) + 2) - 1) - 5) + 3) and g(x) = (-1(2e^(-1(-1(-5x - 3)^2 + 5(-5x - 3) + 2)) - 3) - 1)/(-3(2e^(-1(-1(-5x - 3)^2 + 5(-5x - 3) + 2)) - 3) + 2) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -1|(1(-3|(1((2x - 1)/(1x - 3)))| + 2) - 5) + 1| + 2 and g(x) = -2|(5(5(-2|x - 2| - 3) - 1) - 2) - 2| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -1(5(-2cos(2\u03c0((3(4x^2 - 4x + 4) + 3)/(2(4x^2 - 4x + 4) - 1))) - 3)^2 - 1) - 5 and g(x) = -1(2|(-1e^(2(3|x + 1| - 1)) - 1) - 2| - 1) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (3((1(2e^(1(3|(2|x + 2| - 3) - 3| + 2)) + 3) + 1)/(2(2e^(1(3|(2|x + 2| - 3) - 3| + 2)) + 3) + 2)) + 2)/(2((1(2e^(1(3|(2|x + 2| - 3) - 3| + 2)) + 3) + 1)/(2(2e^(1(3|(2|x + 2| - 3) - 3| + 2)) + 3) + 2)) + 1) and g(x) = (2(-5((1((-1x + 1)/(-1x - 3)))/(2((-1x + 1)/(-1x - 3)) + 2)) + 3) - 3)/(1(-5((1((-1x + 1)/(-1x - 3)))/(2((-1x + 1)/(-1x - 3)) + 2)) + 3) - 3) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 5((2(-4((-1((-1x + 3)/(-3x)))/(3((-1x + 3)/(-3x)) + 2))^2 - 2((-1((-1x + 3)/(-3x)))/(3((-1x + 3)/(-3x)) + 2)) + 5) + 1)/(-3(-4((-1((-1x + 3)/(-3x)))/(3((-1x + 3)/(-3x)) + 2))^2 - 2((-1((-1x + 3)/(-3x)))/(3((-1x + 3)/(-3x)) + 2)) + 5) + 2))^2 + 1((2(-4((-1((-1x + 3)/(-3x)))/(3((-1x + 3)/(-3x)) + 2))^2 - 2((-1((-1x + 3)/(-3x)))/(3((-1x + 3)/(-3x)) + 2)) + 5) + 1)/(-3(-4((-1((-1x + 3)/(-3x)))/(3((-1x + 3)/(-3x)) + 2))^2 - 2((-1((-1x + 3)/(-3x)))/(3((-1x + 3)/(-3x)) + 2)) + 5) + 2)) and g(x) = -5(1(-2(4x)^2 - 3) + 1) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -3|(3|(-4(3|((1x)/(-2x + 3)) - 3| + 1)^2 - 4(3|((1x)/(-2x + 3)) - 3| + 1) + 1) - 3| + 1)| + 1 and g(x) = -2(5(3(-2x + 2)^2 - 4(-2x + 2) - 1)^2 + 5(3(-2x + 2)^2 - 4(-2x + 2) - 1) + 3) - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 3((1((2(3|(-3sin(2\u03c0x + 1) + 1) + 2| - 2) - 1)/(-2(3|(-3sin(2\u03c0x + 1) + 1) + 2| - 2) + 1)) + 3)/(1((2(3|(-3sin(2\u03c0x + 1) + 1) + 2| - 2) - 1)/(-2(3|(-3sin(2\u03c0x + 1) + 1) + 2| - 2) + 1)) - 3)) + 3 and g(x) = 3(3(-3((-2x)/(-1x - 3)) + 4)) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (1((3(-5(-1(-3x^2 + 1x - 3) + 3)^2 - 5(-1(-3x^2 + 1x - 3) + 3) - 4))/(1(-5(-1(-3x^2 + 1x - 3) + 3)^2 - 5(-1(-3x^2 + 1x - 3) + 3) - 4))) + 2)/(3((3(-5(-1(-3x^2 + 1x - 3) + 3)^2 - 5(-1(-3x^2 + 1x - 3) + 3) - 4))/(1(-5(-1(-3x^2 + 1x - 3) + 3)^2 - 5(-1(-3x^2 + 1x - 3) + 3) - 4))) + 3) and g(x) = 1((3(5(5x + 5)) - 2)/(1(5(5x + 5)) + 2)) + 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2e^(-1(-1|(-5(-2(3|x| - 2)^2 - 4(3|x| - 2) - 4) + 2) - 3| - 1)) + 2 and g(x) = 4(3|((2(-2cos(1\u03c0x)) + 3)/(1(-2cos(1\u03c0x)))) - 3| - 1)^2 - 2(3|((2(-2cos(1\u03c0x)) + 3)/(1(-2cos(1\u03c0x)))) - 3| - 1) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = 2|(-1(2|((2(5x + 1) + 3)/(-1(5x + 1) + 3)) - 2| + 3)^2 - 2(2|((2(5x + 1) + 3)/(-1(5x + 1) + 3)) - 2| + 3) + 2) - 1| and g(x) = -3(-1|(-1(5x^2 + 5x - 3)^2 - 4(5x^2 + 5x - 3) + 3) + 3| + 1) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1|(-5(5(2(-1e^(1x) + 1)^2 - 1(-1e^(1x) + 1) + 3)^2 + 1(2(-1e^(1x) + 1)^2 - 1(-1e^(1x) + 1) + 3) + 3) - 2) - 2| - 1 and g(x) = 4(1((3(2e^(1x) - 2) - 2)/(2(2e^(1x) - 2))) + 4) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 4(4((1(-2e^(-1((-3x + 3)/(-2x + 3))) + 2) + 3)/(-2(-2e^(-1((-3x + 3)/(-2x + 3))) + 2) - 1))) - 3 and g(x) = 2|((3(-2e^(-1((-2x - 1)/(2x + 1))) - 2) + 2)/(-1(-2e^(-1((-2x - 1)/(2x + 1))) - 2) - 1)) - 1| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (-1(-2|((-1(-1(-3|x| + 1) + 4) + 1)/(3(-1(-3|x| + 1) + 4) + 3)) - 1| + 1) - 3)/(2(-2|((-1(-1(-3|x| + 1) + 4) + 1)/(3(-1(-3|x| + 1) + 4) + 3)) - 1| + 1) + 1) and g(x) = (1(2|(1(-1x - 1) - 2) + 1| + 1) - 1)/(1(2|(1(-1x - 1) - 2) + 1| + 1)) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3(2((2(4((-1x)/(-3x + 2)) + 3) - 2)/(3(4((-1x)/(-3x + 2)) + 3) + 2))^2) - 5 and g(x) = (3(-2(-5((-1x - 3)/(-2x + 3)) + 2) + 2) - 2)/(-1(-2(-5((-1x - 3)/(-2x + 3)) + 2) + 2) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 3(-3|(-2e^(-1((2(3x^2 - 1x - 3) + 1)/(-2(3x^2 - 1x - 3) - 2)))) - 3| - 3)^2 + 2(-3|(-2e^(-1((2(3x^2 - 1x - 3) + 1)/(-2(3x^2 - 1x - 3) - 2)))) - 3| - 3) + 3 and g(x) = 4(-1|(1(2sin(3\u03c0x - 2) + 3)^2 - 2(2sin(3\u03c0x - 2) + 3) - 3) + 1| - 1)^2 + 4(-1|(1(2sin(3\u03c0x - 2) + 3)^2 - 2(2sin(3\u03c0x - 2) + 3) - 3) + 1| - 1) + 4 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -4(4((-3((-3(5x + 3) - 1)/(-1(5x + 3) + 2)) + 3)/(3((-3(5x + 3) - 1)/(-1(5x + 3) + 2)) + 1)) - 1)^2 - 2(4((-3((-3(5x + 3) - 1)/(-1(5x + 3) + 2)) + 3)/(3((-3(5x + 3) - 1)/(-1(5x + 3) + 2)) + 1)) - 1) + 1 and g(x) = 3e^(-1(5((3(-4x^2 - 4) + 2)/(1(-4x^2 - 4))) - 2)) - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2((-1(-1(4((-2x - 1)/(-1x + 2)) - 1)^2 - 1(4((-2x - 1)/(-1x + 2)) - 1) - 2) - 1)/(2(-1(4((-2x - 1)/(-1x + 2)) - 1)^2 - 1(4((-2x - 1)/(-1x + 2)) - 1) - 2) - 3)) - 1)/(-1((-1(-1(4((-2x - 1)/(-1x + 2)) - 1)^2 - 1(4((-2x - 1)/(-1x + 2)) - 1) - 2) - 1)/(2(-1(4((-2x - 1)/(-1x + 2)) - 1)^2 - 1(4((-2x - 1)/(-1x + 2)) - 1) - 2) - 3)) + 2) and g(x) = (1((-1(5(-5x - 1) + 3) - 2)/(-3(5(-5x - 1) + 3) + 2)) + 3)/(-2((-1(5(-5x - 1) + 3) - 2)/(-3(5(-5x - 1) + 3) + 2)) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 1e^(-1(3|(3|(-5(5x + 2) - 2) - 3|)| - 3)) - 1 and g(x) = (1(2sin(2\u03c0(5(4x - 2) - 1) + 3) + 3))/(-3(2sin(2\u03c0(5(4x - 2) - 1) + 3) + 3) + 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (2(-1|(4(2|((3x)/(3x + 3))| - 1) - 5) + 3| + 2) - 1)/(-2(-1|(4(2|((3x)/(3x + 3))| - 1) - 5) + 3| + 2) + 3) and g(x) = -2|(-3|((-1(-1|x + 2| + 3) + 2)/(3(-1|x + 2| + 3) - 1)) + 2| - 3) - 3| - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 2|((-1(1e^(-1(1((2x - 2)/(-1x + 3))^2 - 4((2x - 2)/(-1x + 3)) - 2)) - 1) + 2)/(-3(1e^(-1(1((2x - 2)/(-1x + 3))^2 - 4((2x - 2)/(-1x + 3)) - 2)) - 1) + 1)) - 3| - 3 and g(x) = -1(2|(-2|((1x + 2)/(3x - 2)) + 1| + 2) - 3| - 1)^2 + 1(2|(-2|((1x + 2)/(3x - 2)) + 1| + 2) - 3| - 1) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (3(2(3(3(2e^(-1x) - 3) - 5) - 1)^2 - 2(3(3(2e^(-1x) - 3) - 5) - 1) + 3))/(-3(2(3(3(2e^(-1x) - 3) - 5) - 1)^2 - 2(3(3(2e^(-1x) - 3) - 5) - 1) + 3) + 2) and g(x) = (2(1|(-1((-3x - 2)/(3x + 1))^2 - 5((-3x - 2)/(3x + 1)) + 4) + 3| + 1) - 1)/(-1(1|(-1((-3x - 2)/(3x + 1))^2 - 5((-3x - 2)/(3x + 1)) + 4) + 3| + 1) - 1) meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3((-2(-3|(-2(-3x - 5) + 2) + 3| + 3) - 1)/(-2(-3|(-2(-3x - 5) + 2) + 3| + 3) + 3))^2 - 2((-2(-3|(-2(-3x - 5) + 2) + 3| + 3) - 1)/(-2(-3|(-2(-3x - 5) + 2) + 3| + 3) + 3)) + 4 and g(x) = -2(2(1(-1cos(2\u03c0x + 1) - 2)^2 - 1(-1cos(2\u03c0x + 1) - 2) - 4)^2 + 2(1(-1cos(2\u03c0x + 1) - 2)^2 - 1(-1cos(2\u03c0x + 1) - 2) - 4) - 2)^2 - 1(2(1(-1cos(2\u03c0x + 1) - 2)^2 - 1(-1cos(2\u03c0x + 1) - 2) - 4)^2 + 2(1(-1cos(2\u03c0x + 1) - 2)^2 - 1(-1cos(2\u03c0x + 1) - 2) - 4) - 2) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-3(3((2((1(-5x^2 - 1x + 4) + 2)/(-3(-5x^2 - 1x + 4))) + 2)/(-3((1(-5x^2 - 1x + 4) + 2)/(-3(-5x^2 - 1x + 4))) + 1)) - 4) - 3)/(-1(3((2((1(-5x^2 - 1x + 4) + 2)/(-3(-5x^2 - 1x + 4))) + 2)/(-3((1(-5x^2 - 1x + 4) + 2)/(-3(-5x^2 - 1x + 4))) + 1)) - 4) - 2) and g(x) = 1(-2cos(1\u03c0((-2(-1x - 3))/(2(-1x - 3) - 1)) + 3) + 3)^2 + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3((-2(-1(1(-3x + 3) - 1)^2 + 4) - 1)/(1(-1(1(-3x + 3) - 1)^2 + 4) - 2)) - 2 and g(x) = (-1(-4(-4(3x^2 - 1x)^2 - 4(3x^2 - 1x) + 3) - 2) - 1)/(-3(-4(-4(3x^2 - 1x)^2 - 4(3x^2 - 1x) + 3) - 2) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 3((-2(-2|(3|((3x - 2)/(-3x - 2)) - 2|) - 2| + 1) + 2)/(-1(-2|(3|((3x - 2)/(-3x - 2)) - 2|) - 2| + 1))) and g(x) = -3sin(2\u03c0(2(-2(-1|x - 1|)^2 + 2(-1|x - 1|) + 4) + 3) - 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 5(1(1|(-3e^(1(-4x - 1)) + 3)| + 1) - 3) + 2 and g(x) = -3|((-1(-5(-3|x - 2| - 1)^2 - 3(-3|x - 2| - 1) - 5) - 1)/(3(-5(-3|x - 2| - 1)^2 - 3(-3|x - 2| - 1) - 5) - 2)) - 2| - 1 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3|(2|(-5((-3((-3x - 2)/(2x - 1)) + 1)/(-1((-3x - 2)/(2x - 1)) + 3))^2 - 2((-3((-3x - 2)/(2x - 1)) + 1)/(-1((-3x - 2)/(2x - 1)) + 3))) - 3| + 3) + 1| - 1 and g(x) = -4(1e^(1((1(3x^2 - 3x - 5) + 2)/(1(3x^2 - 3x - 5) - 3))) - 1) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -2(5(-1(2(-1x^2 + 5x - 4) - 1)^2 + 4(2(-1x^2 + 5x - 4) - 1) + 5) - 5)^2 - 3(5(-1(2(-1x^2 + 5x - 4) - 1)^2 + 4(2(-1x^2 + 5x - 4) - 1) + 5) - 5) + 4 and g(x) = 3(-4(1((3x + 1)/(2x - 1)) - 3) - 3) + 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -1sin(3\u03c0((3(-1(5(-3|x + 2| - 2)^2 - 4(-3|x + 2| - 2) + 5) - 1))/(-2(-1(5(-3|x + 2| - 2)^2 - 4(-3|x + 2| - 2) + 5) - 1) - 1)) - 2) - 3 and g(x) = -1|(3e^(2(2|(-3|x - 2|)| - 3))) + 2| + 1 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = (-3((-1(-3|(1|(1sin(3\u03c0x + 2) + 2) + 3| - 1) + 3| - 3) - 3)/(-1(-3|(1|(1sin(3\u03c0x + 2) + 2) + 3| - 1) + 3| - 3) + 3)) + 1)/(-1((-1(-3|(1|(1sin(3\u03c0x + 2) + 2) + 3| - 1) + 3| - 3) - 3)/(-1(-3|(1|(1sin(3\u03c0x + 2) + 2) + 3| - 1) + 3| - 3) + 3)) - 2) and g(x) = (-1(-1(2|(1x^2 + 3x + 5) - 3|) + 4) + 2)/(2(-1(2|(1x^2 + 3x + 5) - 3|) + 4) - 1) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-2(-1((3(5(2x - 2) + 5))/(-1(5(2x - 2) + 5) + 2))^2 - 4((3(5(2x - 2) + 5))/(-1(5(2x - 2) + 5) + 2)) - 1) + 1)/(1(-1((3(5(2x - 2) + 5))/(-1(5(2x - 2) + 5) + 2))^2 - 4((3(5(2x - 2) + 5))/(-1(5(2x - 2) + 5) + 2)) - 1)) and g(x) = (3(5(-1(-3|x - 1| - 1)^2 + 3(-3|x - 1| - 1))) - 2)/(-2(5(-1(-3|x - 1| - 1)^2 + 3(-3|x - 1| - 1))) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1((-1((-2(-4(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 2) + 1)/(-2(-4(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 2) - 2)) + 1)/(3((-2(-4(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 2) + 1)/(-2(-4(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 2) - 2)) + 3))^2 + 2((-1((-2(-4(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 2) + 1)/(-2(-4(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 2) - 2)) + 1)/(3((-2(-4(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 2) + 1)/(-2(-4(1|x - 2| - 3)^2 + 3(1|x - 2| - 3) + 2) - 2)) + 3)) - 4 and g(x) = 1((-1((2(-2e^(1x) + 2) + 2)/(-1(-2e^(1x) + 2) + 3)) - 2)/(-3((2(-2e^(1x) + 2) + 2)/(-1(-2e^(1x) + 2) + 3)) + 1)) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1|((2(3|(3|(-4x^2 + 1x) + 1| + 1)| + 3))/(-3(3|(3|(-4x^2 + 1x) + 1| + 1)| + 3) - 1)) - 2| + 3 and g(x) = 5(1(-3((-2x - 3)/(-3x - 1)) - 3) - 4)^2 - 3(1(-3((-2x - 3)/(-3x - 1)) - 3) - 4) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3e^(-2((3(-1(-3(-4x + 4) - 1)^2 - 3(-3(-4x + 4) - 1) + 1) - 2)/(2(-1(-3(-4x + 4) - 1)^2 - 3(-3(-4x + 4) - 1) + 1) + 1))) and g(x) = -2(3|(3|(-3cos(1\u03c0x - 3)) - 1|) + 3| + 3) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1e^(2(-2((-2((-3((2x + 1)/(2x + 3)) - 3)/(-1((2x + 1)/(2x + 3)) + 3)) + 2)/(-3((-3((2x + 1)/(2x + 3)) - 3)/(-1((2x + 1)/(2x + 3)) + 3)) + 2)) - 1)) - 1 and g(x) = -1|(-2|((2(-3x^2 + 3x + 3) - 3)/(1(-3x^2 + 3x + 3) + 1)) - 3| - 1) - 2| - 2 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 3(-3(-3((1(1x - 5))/(3(1x - 5) - 1)) - 2) + 1) + 5 and g(x) = 3(-3(-1|(1x - 2) + 3| - 1) - 1) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1(-3((-1((-1(-5x - 2) - 1)/(3(-5x - 2))) + 3)/(-1((-1(-5x - 2) - 1)/(3(-5x - 2))) + 2))^2 - 3((-1((-1(-5x - 2) - 1)/(3(-5x - 2))) + 3)/(-1((-1(-5x - 2) - 1)/(3(-5x - 2))) + 2)) - 1) - 3)/(-1(-3((-1((-1(-5x - 2) - 1)/(3(-5x - 2))) + 3)/(-1((-1(-5x - 2) - 1)/(3(-5x - 2))) + 2))^2 - 3((-1((-1(-5x - 2) - 1)/(3(-5x - 2))) + 3)/(-1((-1(-5x - 2) - 1)/(3(-5x - 2))) + 2)) - 1) - 3) and g(x) = (3(-5(-4(1|x + 3| - 2)^2 - 3(1|x + 3| - 2) - 2) + 3) - 3)/(2(-5(-4(1|x + 3| - 2)^2 - 3(1|x + 3| - 2) - 2) + 3) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = (1((-1(3|(5(-2sin(1\u03c0x + 2))^2 - 3(-2sin(1\u03c0x + 2)) + 2) + 3| + 2) - 3)/(-3(3|(5(-2sin(1\u03c0x + 2))^2 - 3(-2sin(1\u03c0x + 2)) + 2) + 3| + 2))) - 3)/(-3((-1(3|(5(-2sin(1\u03c0x + 2))^2 - 3(-2sin(1\u03c0x + 2)) + 2) + 3| + 2) - 3)/(-3(3|(5(-2sin(1\u03c0x + 2))^2 - 3(-2sin(1\u03c0x + 2)) + 2) + 3| + 2))) + 2) and g(x) = -3e^(2(-5((-3(1x^2 + 2x - 5))/(-2(1x^2 + 2x - 5) - 3)) + 2)) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -2(1|(3e^(1(-5((2x - 2)/(2x))^2 + 4((2x - 2)/(2x)))) + 3)| + 3) - 1 and g(x) = (1(-3|(-1((-1x + 3)/(-2x + 3))^2 - 4((-1x + 3)/(-2x + 3))) + 1| + 2) - 2)/(1(-3|(-1((-1x + 3)/(-2x + 3))^2 - 4((-1x + 3)/(-2x + 3))) + 1| + 2) + 1) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -1(-5(-2(2(-3e^(1x) + 2)) + 5)^2 + 5(-2(2(-3e^(1x) + 2)) + 5) + 5) - 1 and g(x) = (-2(1(1|(-1e^(-1x) + 2) - 3| + 2)) + 1)/(-2(1(1|(-1e^(-1x) + 2) - 3| + 2)) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (2(-3((-1(3|(-1x^2 - 1x + 3) - 3| - 3) + 2)/(-1(3|(-1x^2 - 1x + 3) - 3| - 3) - 1)) - 1) + 1)/(-1(-3((-1(3|(-1x^2 - 1x + 3) - 3| - 3) + 2)/(-1(3|(-1x^2 - 1x + 3) - 3| - 3) - 1)) - 1) + 3) and g(x) = -5(-1(-2cos(2\u03c0(3x^2 + 5)) - 3) - 5) + 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-1(-1(-1|(-4(-4x + 2)^2 - 2(-4x + 2) + 2) + 2| + 3)^2 - 2(-1|(-4(-4x + 2)^2 - 2(-4x + 2) + 2) + 2| + 3)) + 1)/(3(-1(-1|(-4(-4x + 2)^2 - 2(-4x + 2) + 2) + 2| + 3)^2 - 2(-1|(-4(-4x + 2)^2 - 2(-4x + 2) + 2) + 2| + 3))) and g(x) = -5((2((1(2|x - 2|) - 2)/(2(2|x - 2|) + 1)) - 2)/(-1((1(2|x - 2|) - 2)/(2(2|x - 2|) + 1)) + 3)) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 3|(-3|(2e^(-1(4(-2|x + 1| - 3)^2 + 5(-2|x + 1| - 3) + 1)) + 1) - 2|) - 3| - 1 and g(x) = -3(-5((2((-1x + 2)/(2x - 1)) - 2)/(-2((-1x + 2)/(2x - 1)) + 1))) - 2 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 3((-3((3(2e^(1(-2x + 2)) - 3) - 1)/(-2(2e^(1(-2x + 2)) - 3) + 3)) - 2)/(2((3(2e^(1(-2x + 2)) - 3) - 1)/(-2(2e^(1(-2x + 2)) - 3) + 3)) - 3)) - 4 and g(x) = 5(-1((2(-3|x - 3| - 2) - 3)/(3(-3|x - 3| - 2))))^2 + 2(-1((2(-3|x - 3| - 2) - 3)/(3(-3|x - 3| - 2)))) + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 1(-1|(-4(-2|(2|x - 1| + 3)| - 1) - 3) + 1|) + 5 and g(x) = (1(5((1(3x) - 3)/(-2(3x) + 3)) - 5) - 2)/(1(5((1(3x) - 3)/(-2(3x) + 3)) - 5)) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3(2(1((-2(4x^2 + 4x + 3) + 3)/(2(4x^2 + 4x + 3) - 1))^2 - 3((-2(4x^2 + 4x + 3) + 3)/(2(4x^2 + 4x + 3) - 1)) - 3)^2 - 3(1((-2(4x^2 + 4x + 3) + 3)/(2(4x^2 + 4x + 3) - 1))^2 - 3((-2(4x^2 + 4x + 3) + 3)/(2(4x^2 + 4x + 3) - 1)) - 3) + 1) - 4 and g(x) = (-1(-3(-1(-3|x + 2| + 2) + 3)^2 + 5(-1(-3|x + 2| + 2) + 3) - 2))/(-3(-3(-1(-3|x + 2| + 2) + 3)^2 + 5(-1(-3|x + 2| + 2) + 3) - 2) + 1) intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2|((3(4(-4(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 5)^2 + 2(-4(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 5) + 4) - 2)/(1(4(-4(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 5)^2 + 2(-4(1x^2 - 4x)^2 - 1(1x^2 - 4x) - 5) + 4) + 2)) - 3| + 1 and g(x) = (3(1(-1e^(2((3x - 2)/(-1x + 3))) - 1) + 2) + 1)/(2(1(-1e^(2((3x - 2)/(-1x + 3))) - 1) + 2) - 1) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = (-2((-3((-1(1(1|x - 2| - 2)^2 + 3(1|x - 2| - 2) - 3) + 3)/(-2(1(1|x - 2| - 2)^2 + 3(1|x - 2| - 2) - 3))) + 3)/(-2((-1(1(1|x - 2| - 2)^2 + 3(1|x - 2| - 2) - 3) + 3)/(-2(1(1|x - 2| - 2)^2 + 3(1|x - 2| - 2) - 3))))) - 2)/(3((-3((-1(1(1|x - 2| - 2)^2 + 3(1|x - 2| - 2) - 3) + 3)/(-2(1(1|x - 2| - 2)^2 + 3(1|x - 2| - 2) - 3))) + 3)/(-2((-1(1(1|x - 2| - 2)^2 + 3(1|x - 2| - 2) - 3) + 3)/(-2(1(1|x - 2| - 2)^2 + 3(1|x - 2| - 2) - 3)))))) and g(x) = 3|((-2(2e^(-1((1x)/(-3x))) - 3) + 3)/(1(2e^(-1((1x)/(-3x))) - 3) - 2)) + 3| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = (1((1(1|(2cos(2\u03c0((-2x)/(3x + 1)) + 1) - 1) + 2| - 2))/(-1(1|(2cos(2\u03c0((-2x)/(3x + 1)) + 1) - 1) + 2| - 2))) - 3)/(3((1(1|(2cos(2\u03c0((-2x)/(3x + 1)) + 1) - 1) + 2| - 2))/(-1(1|(2cos(2\u03c0((-2x)/(3x + 1)) + 1) - 1) + 2| - 2))) + 2) and g(x) = 1(1|(1|(-2x^2 + 1x + 2) - 2| + 1) + 2|) - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1|(-2(-2sin(1\u03c0(-1|((2x + 3)/(1x - 3))| - 1) - 3) + 2)^2 - 2(-2sin(1\u03c0(-1|((2x + 3)/(1x - 3))| - 1) - 3) + 2) - 4) - 1| + 1 and g(x) = 5((3(1|((-2x + 2)/(2x - 1)) + 2| - 1))/(1(1|((-2x + 2)/(2x - 1)) + 2| - 1) + 3)) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 3((3(-3(-2(-4x + 4) - 1) + 2) - 1)/(-2(-3(-2(-4x + 4) - 1) + 2) + 1))^2 + 4((3(-3(-2(-4x + 4) - 1) + 2) - 1)/(-2(-3(-2(-4x + 4) - 1) + 2) + 1)) - 5 and g(x) = (1(3|(-3sin(2\u03c0((2x - 1)/(2x - 1))) + 2)| + 2) + 3)/(3(3|(-3sin(2\u03c0((2x - 1)/(2x - 1))) + 2)| + 2) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (1(-1(2|((3((3x + 1)/(2x - 1)) - 1)/(-1((3x + 1)/(2x - 1)) + 2))| - 2) - 2) + 2)/(-3(-1(2|((3((3x + 1)/(2x - 1)) - 1)/(-1((3x + 1)/(2x - 1)) + 2))| - 2) - 2) + 2) and g(x) = -2(5(-4((-1x - 2)/(3x - 2)) + 5) + 5) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 3(-5((-1((1(-2x^2 - 4x - 4) + 3)/(-1(-2x^2 - 4x - 4) - 3)) - 3)/(-1((1(-2x^2 - 4x - 4) + 3)/(-1(-2x^2 - 4x - 4) - 3)) + 2)) - 2) - 4 and g(x) = -1(2e^(2((1((1x - 3)/(-1x + 2)))/(-3((1x - 3)/(-1x + 2)) + 1))) - 2)^2 + 5(2e^(2((1((1x - 3)/(-1x + 2)))/(-3((1x - 3)/(-1x + 2)) + 1))) - 2) + 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 5(1|((-3(2|(-1x^2 + 1x + 2) + 1| + 2) + 1)/(-1(2|(-1x^2 + 1x + 2) + 1| + 2) + 2)) - 2| + 1)^2 + 1(1|((-3(2|(-1x^2 + 1x + 2) + 1| + 2) + 1)/(-1(2|(-1x^2 + 1x + 2) + 1| + 2) + 2)) - 2| + 1) - 1 and g(x) = (-1(1(1(-3|x - 2| - 2) + 5) + 3) + 1)/(-3(1(1(-3|x - 2| - 2) + 5) + 3) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (-2(3|(-1|(1sin(3\u03c0(1|x + 3| + 2)) - 1) - 3| + 2) + 1| + 3) - 1)/(1(3|(-1|(1sin(3\u03c0(1|x + 3| + 2)) - 1) - 3| + 2) + 1| + 3) + 2) and g(x) = 1(-2|((-2(-2x + 3))/(-2(-2x + 3) + 3)) + 2| + 1)^2 - 3(-2|((-2(-2x + 3))/(-2(-2x + 3) + 3)) + 2| + 1) - 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -5(1(-4(2e^(1(-1x^2 - 1x + 1)) - 3)) - 1) + 2 and g(x) = (1(5(-3|(1x^2 + 3x - 5) - 2| - 3)^2 + 5(-3|(1x^2 + 3x - 5) - 2| - 3) - 3) - 3)/(1(5(-3|(1x^2 + 3x - 5) - 2| - 3)^2 + 5(-3|(1x^2 + 3x - 5) - 2| - 3) - 3) - 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 4((1(5((-1(4x^2 + 3x - 5))/(-3(4x^2 + 3x - 5) + 1))) - 3)/(3(5((-1(4x^2 + 3x - 5))/(-3(4x^2 + 3x - 5) + 1))) - 2)) - 1 and g(x) = -1cos(3\u03c0((-1(3(-3|x + 3| - 3) + 1) - 3)/(-3(3(-3|x + 3| - 3) + 1))) - 1) + 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (2(1(-4(-2e^(-2((-2x - 2)/(-3x + 1))))^2 + 1(-2e^(-2((-2x - 2)/(-3x + 1)))) + 3)^2 - 4(-4(-2e^(-2((-2x - 2)/(-3x + 1))))^2 + 1(-2e^(-2((-2x - 2)/(-3x + 1)))) + 3) - 5) + 3)/(-3(1(-4(-2e^(-2((-2x - 2)/(-3x + 1))))^2 + 1(-2e^(-2((-2x - 2)/(-3x + 1)))) + 3)^2 - 4(-4(-2e^(-2((-2x - 2)/(-3x + 1))))^2 + 1(-2e^(-2((-2x - 2)/(-3x + 1)))) + 3) - 5) + 1) and g(x) = 2(-2(3sin(3\u03c0(2|x + 3| - 3) - 1) + 1) - 4)^2 - 4(-2(3sin(3\u03c0(2|x + 3| - 3) - 1) + 1) - 4) + 2 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3(-2(2(-1e^(-2(-3x^2 + 5)) - 1)^2 - 3(-1e^(-2(-3x^2 + 5)) - 1) - 5) - 3)^2 + 1(-2(2(-1e^(-2(-3x^2 + 5)) - 1)^2 - 3(-1e^(-2(-3x^2 + 5)) - 1) - 5) - 3) - 3 and g(x) = -5(-2|(-1((-3x + 3)/(1x))^2 + 2((-3x + 3)/(1x)) - 3) - 1| + 2)^2 - 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = (3(1|(1|(-4((-3x + 1)/(1x + 3))^2 - 4((-3x + 1)/(1x + 3)) - 1) - 2| - 2)| - 1) - 3)/(1(1|(1|(-4((-3x + 1)/(1x + 3))^2 - 4((-3x + 1)/(1x + 3)) - 1) - 2| - 2)| - 1)) and g(x) = 1|((-2(-2|((-3x + 2)/(-3x + 2))| + 3) + 2)/(-3(-2|((-3x + 2)/(-3x + 2))| + 3) - 3)) + 2| - 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -2(-1(-2e^(1((-1((2x + 1)/(-1x + 2)) + 3)/(3((2x + 1)/(-1x + 2)) - 2))) - 1)^2 + 4) + 5 and g(x) = -1|(3|((-1(-1|x - 2| + 2) - 3)/(2(-1|x - 2| + 2) + 2)) - 3| + 2) - 3| + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = -4(3|((-2(2cos(1\u03c0(-1|x + 2| - 2) - 1) + 3) + 2)/(-3(2cos(1\u03c0(-1|x + 2| - 2) - 1) + 3) - 3)) + 2| - 3) - 3 and g(x) = (-1((2(-1((2x - 2)/(1x + 2)) - 5) + 3)/(1(-1((2x - 2)/(1x + 2)) - 5) - 2)) - 2)/(3((2(-1((2x - 2)/(1x + 2)) - 5) + 3)/(1(-1((2x - 2)/(1x + 2)) - 5) - 2)) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -4(2sin(3\u03c0(-2((1((-3x - 3)/(-2x - 1)) - 1)/(-2((-3x - 3)/(-2x - 1)) - 1)) - 5) - 2)) + 5 and g(x) = -1(-4(-1(5x - 4)^2 - 1(5x - 4) - 1)^2 + 4(-1(5x - 4)^2 - 1(5x - 4) - 1) - 4) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -1(3(-1((1(-3x + 5) - 2)/(2(-3x + 5) + 2)) - 1)^2 + 2(-1((1(-3x + 5) - 2)/(2(-3x + 5) + 2)) - 1) - 3)^2 - 3(3(-1((1(-3x + 5) - 2)/(2(-3x + 5) + 2)) - 1)^2 + 2(-1((1(-3x + 5) - 2)/(2(-3x + 5) + 2)) - 1) - 3) + 5 and g(x) = -2|(1(3(2|x + 3| - 3)^2 - 5(2|x + 3| - 3) + 2)^2 - 4(3(2|x + 3| - 3)^2 - 5(2|x + 3| - 3) + 2)) + 2| + 2 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 5(-3cos(1\u03c0(1(-3|((-2x - 2)/(-3x - 2))| - 1) + 3) - 2)) + 2 and g(x) = 3(1|(-5((-2x + 3)/(3x - 1))^2 - 3) + 2| + 3) meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (3(3(5(1(1|x - 3| - 2) + 1) + 1)) + 3)/(1(3(5(1(1|x - 3| - 2) + 1) + 1))) and g(x) = -2|((-1(1|(2cos(1\u03c0x + 2) - 3) + 3| + 2) - 3)/(-2(1|(2cos(1\u03c0x + 2) - 3) + 3| + 2) + 3)) - 2| meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 2e^(-1((2(-3|(-2|(1|x + 3| - 1) - 3| + 3) - 1|) - 3)/(2(-3|(-2|(1|x + 3| - 1) - 3| + 3) - 1|) + 1))) - 3 and g(x) = -3(3((3((-1x - 1)/(2x - 3)) - 3)/(-3((-1x - 1)/(2x - 3)) - 2)) + 5) + 3 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-1(3(-2|((1(-2x^2 - 1x + 4) + 1)/(-1(-2x^2 - 1x + 4) + 3)) - 2|)^2 + 3(-2|((1(-2x^2 - 1x + 4) + 1)/(-1(-2x^2 - 1x + 4) + 3)) - 2|) + 2))/(2(3(-2|((1(-2x^2 - 1x + 4) + 1)/(-1(-2x^2 - 1x + 4) + 3)) - 2|)^2 + 3(-2|((1(-2x^2 - 1x + 4) + 1)/(-1(-2x^2 - 1x + 4) + 3)) - 2|) + 2) - 1) and g(x) = (1(4(4((3x - 1)/(1x - 2)) + 4) + 1))/(1(4(4((3x - 1)/(1x - 2)) + 4) + 1) + 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-1(1|(-2(2|(-1|x + 2| - 3) - 1|)^2 + 4(2|(-1|x + 2| - 3) - 1|) + 2) - 3| - 1) - 2)/(-2(1|(-2(2|(-1|x + 2| - 3) - 1|)^2 + 4(2|(-1|x + 2| - 3) - 1|) + 2) - 3| - 1)) and g(x) = -1|(-2((-1(1e^(-2x) - 3) - 3)/(-2(1e^(-2x) - 3) + 3))^2)| + 1 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1|(3|(2(-1(1cos(2\u03c0x + 3) + 1) + 1)^2 - 2(-1(1cos(2\u03c0x + 3) + 1) + 1) - 5) + 3| - 3)| - 3 and g(x) = -3|(1((1(-2e^(2x)) - 2)/(2(-2e^(2x)) + 3)) + 4) + 3| + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -4((1(1|(-4((-1x + 1)/(3x + 2)) - 3)| + 1) - 1)/(-1(1|(-4((-1x + 1)/(3x + 2)) - 3)| + 1) + 3)) - 2 and g(x) = 4(-3(-1sin(1\u03c0(-1x - 2) + 3) - 3) - 2) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-1((2(1(-1(-5x + 1) - 3)^2 - 5(-1(-5x + 1) - 3) - 3) - 2)/(-2(1(-1(-5x + 1) - 3)^2 - 5(-1(-5x + 1) - 3) - 3) + 1)) + 3)/(3((2(1(-1(-5x + 1) - 3)^2 - 5(-1(-5x + 1) - 3) - 3) - 2)/(-2(1(-1(-5x + 1) - 3)^2 - 5(-1(-5x + 1) - 3) - 3) + 1)) + 2) and g(x) = 1|(3|(2e^(-1((-3x - 2)/(-2x + 3))) - 3) - 3| - 3)| + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -4(-1|((2(2(-1|x - 1| - 3)^2 + 2(-1|x - 1| - 3) + 4) - 1)/(3(2(-1|x - 1| - 3)^2 + 2(-1|x - 1| - 3) + 4))) + 2| - 1)^2 - 4(-1|((2(2(-1|x - 1| - 3)^2 + 2(-1|x - 1| - 3) + 4) - 1)/(3(2(-1|x - 1| - 3)^2 + 2(-1|x - 1| - 3) + 4))) + 2| - 1) - 3 and g(x) = 4(2((-2((2x - 3)/(-2x - 3)) + 2)/(-1((2x - 3)/(-2x - 3)) + 2)) + 1) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the second intersection point (counting from left to right) between the functions f(x) = 1(-3(-5((-1((-3x - 2)/(1x + 3)) - 3)/(2((-3x - 2)/(1x + 3)) - 1))^2 + 3((-1((-3x - 2)/(1x + 3)) - 3)/(2((-3x - 2)/(1x + 3)) - 1)) + 4))^2 + 5(-3(-5((-1((-3x - 2)/(1x + 3)) - 3)/(2((-3x - 2)/(1x + 3)) - 1))^2 + 3((-1((-3x - 2)/(1x + 3)) - 3)/(2((-3x - 2)/(1x + 3)) - 1)) + 4)) + 1 and g(x) = 3(-3(-1|(3x + 4) - 1| + 1) + 2)^2 - 5(-3(-1|(3x + 4) - 1| + 1) + 2) + 4 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3((-3(4((-2((-2x + 3)/(-2x + 3)) + 2)/(1((-2x + 3)/(-2x + 3)) - 2)) + 2) + 2)/(-1(4((-2((-2x + 3)/(-2x + 3)) + 2)/(1((-2x + 3)/(-2x + 3)) - 2)) + 2) - 3)) + 4 and g(x) = -3(4(2(2e^(1x) - 2)^2 - 1(2e^(1x) - 2) + 1) - 4)^2 - 5(4(2(2e^(1x) - 2)^2 - 1(2e^(1x) - 2) + 1) - 4) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = (-2(3(2e^(-2(-3|((-2x + 3)/(1x - 3)) + 2| + 2)) - 3) - 3) + 2)/(-1(3(2e^(-2(-3|((-2x + 3)/(1x - 3)) + 2| + 2)) - 3) - 3)) and g(x) = -1(-1(2|((2x + 1)/(3x - 1)) - 1| + 1) - 4) - 3 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(1sin(3\u03c0(-2|(-1|(3x^2 + 2) - 2| + 1) + 3| - 3) - 1) + 2) + 5 and g(x) = 1((2((1(5x + 1) - 1)/(3(5x + 1) - 2)) - 1)/(2((1(5x + 1) - 1)/(3(5x + 1) - 2)) + 3))^2 + 1((2((1(5x + 1) - 1)/(3(5x + 1) - 2)) - 1)/(2((1(5x + 1) - 1)/(3(5x + 1) - 2)) + 3)) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -4(1e^(1(4(-3(-3x + 4) - 4)^2 - 3(-3(-3x + 4) - 4) + 1)) - 1)^2 + 1 and g(x) = -2sin(1\u03c0(1(-1|((2x + 1)/(-3x + 1)) - 3|)^2 - 3) + 3) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1(1(-5((2(-4x - 2) + 1)/(-1(-4x - 2))) - 4)^2 + 4(-5((2(-4x - 2) + 1)/(-1(-4x - 2))) - 4) + 2)^2 - 1(1(-5((2(-4x - 2) + 1)/(-1(-4x - 2))) - 4)^2 + 4(-5((2(-4x - 2) + 1)/(-1(-4x - 2))) - 4) + 2) - 3 and g(x) = -1|(1(-1e^(-2((-2x - 2)/(-3x - 1)))) + 5) + 1| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2|((-1(4((3((-2x + 1)/(3x + 2)) - 2)/(-2((-2x + 1)/(3x + 2)) - 2)) + 3) + 1)/(3(4((3((-2x + 1)/(3x + 2)) - 2)/(-2((-2x + 1)/(3x + 2)) - 2)) + 3) - 1)) - 2| - 3 and g(x) = (1(2|(-1|((3x + 3)/(-2x + 3)) + 2| - 3) + 1| + 1) - 2)/(-1(2|(-1|((3x + 3)/(-2x + 3)) + 2| - 3) + 1| + 1)) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2|(-3cos(1\u03c0(-1(-3((3x + 1)/(1x + 3)) + 3) + 2) - 2) - 2) - 2| - 3 and g(x) = 5(3|(-5(-1x - 1) + 4) - 1| + 2) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2sin(1\u03c0((3(3(-1|((1x)/(3x)) + 1| - 2) - 2) + 2)/(-2(3(-1|((1x)/(3x)) + 1| - 2) - 2) - 3)) + 3) - 1 and g(x) = (-3(-1|((-1(-4x - 4) + 2)/(-2(-4x - 4) + 1)) + 2| + 3) - 3)/(1(-1|((-1(-4x - 4) + 2)/(-2(-4x - 4) + 1)) + 2| + 3) - 3) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3((2(-2sin(2\u03c0((1(2|x - 1| + 2) - 1)/(-2(2|x - 1| + 2) - 3)) - 1) + 2) - 2)/(-1(-2sin(2\u03c0((1(2|x - 1| + 2) - 1)/(-2(2|x - 1| + 2) - 3)) - 1) + 2))) + 3 and g(x) = 1|(4(1|(1x^2 - 5x + 4) - 2|) + 5) + 1| meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = 2(-5(1((-3(1|x| + 1) + 2)/(-3(1|x| + 1))) - 2) - 5) + 4 and g(x) = -3((-2(-4((-3x)/(-2x - 3)) + 2) + 2)/(-2(-4((-3x)/(-2x - 3)) + 2) - 1)) - 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -3(-2|(4(-3(5x^2 - 1x - 4)^2 - 2(5x^2 - 1x - 4) + 3) - 1)| + 1)^2 + 1(-2|(4(-3(5x^2 - 1x - 4)^2 - 2(5x^2 - 1x - 4) + 3) - 1)| + 1) - 5 and g(x) = 1(-3((2(-2|x + 1|) - 3)/(3(-2|x + 1|))) + 3) + 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1((-2(-5(2(-1x) - 1)^2 - 1(2(-1x) - 1) - 1) - 3)/(-2(-5(2(-1x) - 1)^2 - 1(2(-1x) - 1) - 1) - 1))^2 - 5((-2(-5(2(-1x) - 1)^2 - 1(2(-1x) - 1) - 1) - 3)/(-2(-5(2(-1x) - 1)^2 - 1(2(-1x) - 1) - 1) - 1)) + 2 and g(x) = -3(-1|((3(-5x - 2))/(-1(-5x - 2) - 2)) - 2| + 2) + 4 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the sum of all x-coordinates (rounded to the nearest integer) where f(x) = -3|(-2(1|(2|((1x + 2)/(1x)) + 2| - 1) + 2| - 2) + 4) + 3| + 1 and g(x) = -5(2|((-3(1x^2 + 5x - 1) + 1)/(2(1x^2 + 5x - 1) + 1)) + 3| + 1)^2 - 3(2|((-3(1x^2 + 5x - 1) + 1)/(2(1x^2 + 5x - 1) + 1)) + 3| + 1) - 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1(3|(4(-2((3x - 2)/(1x)) + 2) - 4) + 1| + 1)^2 + 5(3|(4(-2((3x - 2)/(1x)) + 2) - 4) + 1| + 1) + 5 and g(x) = 5(2sin(1\u03c0(3|(-1|x| + 3) + 1| - 3) + 3) - 1)^2 - 5(2sin(1\u03c0(3|(-1|x| + 3) + 1| - 3) + 3) - 1) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1((3(5(-2sin(1\u03c0(-3x^2 + 4x - 3) + 3)) + 2) - 3)/(-2(5(-2sin(1\u03c0(-3x^2 + 4x - 3) + 3)) + 2) - 1)) - 4 and g(x) = 4(3((3((3x - 3)/(3x + 2)) + 3)/(-1((3x - 3)/(3x + 2)) - 1))^2 + 2((3((3x - 3)/(3x + 2)) + 3)/(-1((3x - 3)/(3x + 2)) - 1)) + 3) - 5 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1(-1|(5((-3(4x - 4) + 1)/(-1(4x - 4) + 3)) + 3)| + 1) + 4 and g(x) = -3|(-5(1(-1|x + 2| - 2)^2 - 2(-1|x + 2| - 2) - 2) + 2) + 1| + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4(-1|(-5(-4(-1x) + 3)^2 + 2(-4(-1x) + 3) - 1) + 3| + 1)^2 + 1(-1|(-5(-4(-1x) + 3)^2 + 2(-4(-1x) + 3) - 1) + 3| + 1) + 1 and g(x) = 3|(-3|(4((2x + 1)/(3x + 3))^2 - 3((2x + 1)/(3x + 3)) - 4) - 1| + 2) + 3| - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 1(2|(1(-5((-2x + 2)/(1x + 1)) - 1) + 3)| - 2)^2 - 4(2|(1(-5((-2x + 2)/(1x + 1)) - 1) + 3)| - 2) + 3 and g(x) = 5(-1(1(-5x + 2) + 4)^2 + 2(1(-5x + 2) + 4) - 3)^2 - 2(-1(1(-5x + 2) + 4)^2 + 2(1(-5x + 2) + 4) - 3) - 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 2(2|(1|(1(3|x + 1| - 1)^2 - 3(3|x + 1| - 1) + 5) - 1|) - 1|)^2 - 2(2|(1|(1(3|x + 1| - 1)^2 - 3(3|x + 1| - 1) + 5) - 1|) - 1|) + 3 and g(x) = 5(1|(4(3|x - 3| + 1)^2 - 5(3|x - 3| + 1) - 4) - 3| - 1)^2 - 4(1|(4(3|x - 3| + 1)^2 - 5(3|x - 3| + 1) - 4) - 3| - 1) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2(3(-5((-2((1x + 3)/(2x - 1)) - 3)/(-1((1x + 3)/(2x - 1)) - 1)) + 4) + 3) - 2)/(-3(3(-5((-2((1x + 3)/(2x - 1)) - 3)/(-1((1x + 3)/(2x - 1)) - 1)) + 4) + 3) + 2) and g(x) = 5(2e^(2((-3(3x^2 + 2x - 2) + 3)/(-1(3x^2 + 2x - 2) - 1))) - 1) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (-2(1(1|(-2(1x - 1)^2 - 1(1x - 1) + 4) + 2| - 2)^2 - 5(1|(-2(1x - 1)^2 - 1(1x - 1) + 4) + 2| - 2) + 5) + 3)/(-3(1(1|(-2(1x - 1)^2 - 1(1x - 1) + 4) + 2| - 2)^2 - 5(1|(-2(1x - 1)^2 - 1(1x - 1) + 4) + 2| - 2) + 5) + 1) and g(x) = -1(-3|(1|(-1|x| + 3) - 3| + 3) + 2| + 1)^2 + 5(-3|(1|(-1|x| + 3) - 3| + 3) + 2| + 1) - 1 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -1|(5(1e^(-1(2(-1|x - 1|) + 1)) + 1) - 4) - 1| - 1 and g(x) = (1(-1(-5(4x^2 - 4x - 2) + 1) - 5) + 3)/(3(-1(-5(4x^2 - 4x - 2) + 1) - 5) + 2) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 5(2(-1((-1((2x)/(2x - 1)) - 2)/(2((2x)/(2x - 1)) - 1))^2 - 5((-1((2x)/(2x - 1)) - 2)/(2((2x)/(2x - 1)) - 1)) - 2)^2 + 4(-1((-1((2x)/(2x - 1)) - 2)/(2((2x)/(2x - 1)) - 1))^2 - 5((-1((2x)/(2x - 1)) - 2)/(2((2x)/(2x - 1)) - 1)) - 2) - 3)^2 + 2(2(-1((-1((2x)/(2x - 1)) - 2)/(2((2x)/(2x - 1)) - 1))^2 - 5((-1((2x)/(2x - 1)) - 2)/(2((2x)/(2x - 1)) - 1)) - 2)^2 + 4(-1((-1((2x)/(2x - 1)) - 2)/(2((2x)/(2x - 1)) - 1))^2 - 5((-1((2x)/(2x - 1)) - 2)/(2((2x)/(2x - 1)) - 1)) - 2) - 3) and g(x) = 2((1(-2(3cos(1\u03c0x - 2) + 1) - 3) - 3)/(1(-2(3cos(1\u03c0x - 2) + 1) - 3))) - 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-3(-1|(-2|(-1|((-3x + 3)/(3x)) + 3| + 3) + 2| + 2) + 1| - 1) + 1)/(2(-1|(-2|(-1|((-3x + 3)/(3x)) + 3| + 3) + 2| + 2) + 1| - 1) - 3) and g(x) = 1|(-2|(-1|(2x^2 - 4x) - 3| + 2) + 3| + 2) + 3| - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -4(2((1(1|(-2e^(2x) + 3) + 3|) - 1)/(-3(1|(-2e^(2x) + 3) + 3|) + 1))^2 - 5((1(1|(-2e^(2x) + 3) + 3|) - 1)/(-3(1|(-2e^(2x) + 3) + 3|) + 1)) - 5) + 3 and g(x) = 1(-4(1e^(2(1x^2 + 1x - 4)) - 3) + 1) + 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -3|(-2|(1((-3(-5x^2 - 1x - 2) - 3)/(-1(-5x^2 - 1x - 2) - 2))^2 + 3((-3(-5x^2 - 1x - 2) - 3)/(-1(-5x^2 - 1x - 2) - 2)) + 5)| + 1) - 2| + 2 and g(x) = -3(3((-3(-4x - 3) + 1)/(2(-4x - 3) - 3)) - 4) intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -1((-2(-1(-2(-1|x + 2| - 1)^2 - 1(-1|x + 2| - 1) - 3) - 4) + 1)/(-3(-1(-2(-1|x + 2| - 1)^2 - 1(-1|x + 2| - 1) - 3) - 4) - 2)) + 3 and g(x) = (2(2(-2|((1x - 3)/(1x)) + 3|) + 1) + 3)/(-1(2(-2|((1x - 3)/(1x)) + 3|) + 1) + 2) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -2((-1((1(2|((-1x - 1)/(2x + 1)) + 3| - 1) - 1)/(-2(2|((-1x - 1)/(2x + 1)) + 3| - 1) - 2)) + 1)/(-1((1(2|((-1x - 1)/(2x + 1)) + 3| - 1) - 1)/(-2(2|((-1x - 1)/(2x + 1)) + 3| - 1) - 2)) - 2)) - 2 and g(x) = -1sin(2\u03c0(1|(-3|(-1x^2 + 5x + 1) - 2| - 2) + 2| - 3) + 2) - 2 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 3|(2|((3(3e^(-1((-1x - 2)/(-2x - 2)))) - 3)/(-3(3e^(-1((-1x - 2)/(-2x - 2)))) + 4)) - 2| + 2)| and g(x) = 4((-3(1(2x + 4)^2 + 5) - 2)/(-1(1(2x + 4)^2 + 5) - 1))^2 - 4((-3(1(2x + 4)^2 + 5) - 2)/(-1(1(2x + 4)^2 + 5) - 1)) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2|((-3((-2((-3(-2x) + 3)/(1(-2x))) + 2)/(-3((-3(-2x) + 3)/(1(-2x))) - 2)) - 3)/(-1((-2((-3(-2x) + 3)/(1(-2x))) + 2)/(-3((-3(-2x) + 3)/(1(-2x))) - 2)) - 3)) - 3| - 3 and g(x) = -1|(1e^(-1((-2(-5x^2 + 4x - 5) - 1)/(-1(-5x^2 + 4x - 5) + 3)))) - 1| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 1(5(-1((-2(1e^(-1x) - 1) - 3)/(3(1e^(-1x) - 1) + 2))^2 - 5((-2(1e^(-1x) - 1) - 3)/(3(1e^(-1x) - 1) + 2)) + 1) - 2) + 1 and g(x) = -1cos(2\u03c0((-3((-2((3x + 2)/(-2x - 2)) - 2)/(3((3x + 2)/(-2x - 2)))) - 1)/(-1((-2((3x + 2)/(-2x - 2)) - 2)/(3((3x + 2)/(-2x - 2)))) + 3)) - 2) - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (3(1(-1|((-3(-3x^2 - 3x + 2) + 3)/(2(-3x^2 - 3x + 2) - 3))|) + 5) - 1)/(2(1(-1|((-3(-3x^2 - 3x + 2) + 3)/(2(-3x^2 - 3x + 2) - 3))|) + 5) - 3) and g(x) = -4(-3e^(-1(1(5x - 2)^2 + 2(5x - 2) - 2)) - 2)^2 + 1(-3e^(-1(1(5x - 2)^2 + 2(5x - 2) - 2)) - 2) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -1e^(-1((-2((-3(3((2x - 1)/(2x - 3))^2 + 1((2x - 1)/(2x - 3)) - 1) - 2)/(3(3((2x - 1)/(2x - 3))^2 + 1((2x - 1)/(2x - 3)) - 1) + 3)) - 3)/(1((-3(3((2x - 1)/(2x - 3))^2 + 1((2x - 1)/(2x - 3)) - 1) - 2)/(3(3((2x - 1)/(2x - 3))^2 + 1((2x - 1)/(2x - 3)) - 1) + 3))))) + 3 and g(x) = -1(-3|((2((2x + 3)/(3x - 1)))/(-3((2x + 3)/(3x - 1)) - 3)) - 2| + 1)^2 - 1(-3|((2((2x + 3)/(3x - 1)))/(-3((2x + 3)/(3x - 1)) - 3)) - 2| + 1) - 5 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3|(-3(-1|((-3(-2|x + 3| + 3) - 2)/(-2(-2|x + 3| + 3) + 3)) - 2| + 3)) - 1| + 2 and g(x) = 5(-4((-3(1e^(2x) + 1) - 3)/(1(1e^(2x) + 1))) + 3)^2 - 1(-4((-3(1e^(2x) + 1) - 3)/(1(1e^(2x) + 1))) + 3) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 3((-3(2(-5((3x + 3)/(-3x + 2)) + 4)^2 - 4(-5((3x + 3)/(-3x + 2)) + 4) + 3) - 3)/(-2(2(-5((3x + 3)/(-3x + 2)) + 4)^2 - 4(-5((3x + 3)/(-3x + 2)) + 4) + 3) - 1))^2 - 5((-3(2(-5((3x + 3)/(-3x + 2)) + 4)^2 - 4(-5((3x + 3)/(-3x + 2)) + 4) + 3) - 3)/(-2(2(-5((3x + 3)/(-3x + 2)) + 4)^2 - 4(-5((3x + 3)/(-3x + 2)) + 4) + 3) - 1)) + 4 and g(x) = 3|(2|(4(-1x + 5)^2 + 2(-1x + 5) + 3) - 2| + 1) - 2| intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1|(2|(-5(-3sin(1\u03c0(-1x^2 + 1x + 1) - 1) + 1) - 2)| + 1) + 2| - 2 and g(x) = 2cos(2\u03c0(1((1(-4x^2 + 1x + 2) - 3)/(3(-4x^2 + 1x + 2)))^2 + 1((1(-4x^2 + 1x + 2) - 3)/(3(-4x^2 + 1x + 2))) - 1) - 3) - 1 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (-2((1((-2(-2(-3x - 2)) + 3)/(3(-2(-3x - 2)) + 3)) + 2)/(3((-2(-2(-3x - 2)) + 3)/(3(-2(-3x - 2)) + 3)) - 2)) - 2)/(2((1((-2(-2(-3x - 2)) + 3)/(3(-2(-3x - 2)) + 3)) + 2)/(3((-2(-2(-3x - 2)) + 3)/(3(-2(-3x - 2)) + 3)) - 2)) - 1) and g(x) = 3(1(3|(-1x^2 + 3x + 4)| + 2))^2 - 3(1(3|(-1x^2 + 3x + 4)| + 2)) + 3 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = (1(3|((1(1(-3x - 4) + 2) - 1)/(1(1(-3x - 4) + 2) - 3)) + 3| - 3))/(-3(3|((1(1(-3x - 4) + 2) - 1)/(1(1(-3x - 4) + 2) - 3)) + 3| - 3) + 4) and g(x) = (1(4(-2sin(3\u03c0(5x^2 - 1x + 5) - 3))^2 + 1(-2sin(3\u03c0(5x^2 - 1x + 5) - 3)) + 2) - 1)/(-1(4(-2sin(3\u03c0(5x^2 - 1x + 5) - 3))^2 + 1(-2sin(3\u03c0(5x^2 - 1x + 5) - 3)) + 2) + 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -2(-1((2((-1(1cos(2\u03c0x - 2)) + 2)/(-1(1cos(2\u03c0x - 2)) - 3)) - 2)/(1((-1(1cos(2\u03c0x - 2)) + 2)/(-1(1cos(2\u03c0x - 2)) - 3)) - 2)) + 5)^2 + 1(-1((2((-1(1cos(2\u03c0x - 2)) + 2)/(-1(1cos(2\u03c0x - 2)) - 3)) - 2)/(1((-1(1cos(2\u03c0x - 2)) + 2)/(-1(1cos(2\u03c0x - 2)) - 3)) - 2)) + 5) + 3 and g(x) = -1(-3|(3(1x) + 5) + 2|)^2 + 5(-3|(3(1x) + 5) + 2|) + 5 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1|((2(-2(-1e^(1(-4x + 4)) - 2) - 5) - 3)/(1(-2(-1e^(1(-4x + 4)) - 2) - 5) - 3)) + 1| + 3 and g(x) = (-3((2((-3((1x + 2)/(-1x - 3)) + 3)/(2((1x + 2)/(-1x - 3)) + 2)) - 1)/(-1((-3((1x + 2)/(-1x - 3)) + 3)/(2((1x + 2)/(-1x - 3)) + 2)) - 3)) + 1)/(-3((2((-3((1x + 2)/(-1x - 3)) + 3)/(2((1x + 2)/(-1x - 3)) + 2)) - 1)/(-1((-3((1x + 2)/(-1x - 3)) + 3)/(2((1x + 2)/(-1x - 3)) + 2)) - 3)) - 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -2(4(-2|(-4(-1|x + 3| + 3)^2 - 1(-1|x + 3| + 3) - 1) + 1|)^2 - 1(-2|(-4(-1|x + 3| + 3)^2 - 1(-1|x + 3| + 3) - 1) + 1|) + 1)^2 - 4(4(-2|(-4(-1|x + 3| + 3)^2 - 1(-1|x + 3| + 3) - 1) + 1|)^2 - 1(-2|(-4(-1|x + 3| + 3)^2 - 1(-1|x + 3| + 3) - 1) + 1|) + 1) + 4 and g(x) = 1(1(3(-3e^(1x) - 1)^2 + 1(-3e^(1x) - 1) - 1) - 3)^2 + 2(1(3(-3e^(1x) - 1)^2 + 1(-3e^(1x) - 1) - 1) - 3) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-6", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2(2(-1|(3sin(1\u03c0(4x + 2) + 3) + 2) + 1| - 3) - 2) + 2 and g(x) = 1(-1|((2((-1x)/(2x - 1)) + 1)/(3((-1x)/(2x - 1)) + 2)) + 1| - 1)^2 + 3(-1|((2((-1x)/(2x - 1)) + 1)/(3((-1x)/(2x - 1)) + 2)) + 1| - 1) - 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 5(1|(1|(-3|((2x + 3)/(-2x + 3)) - 2|) + 2| - 3) + 1| - 2)^2 - 5(1|(1|(-3|((2x + 3)/(-2x + 3)) - 2|) + 2| - 3) + 1| - 2) - 3 and g(x) = -3(4(-3(-5x - 1) - 5)^2 + 4(-3(-5x - 1) - 5) - 2) + 4 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = -3(3((-1((-1(-2e^(2x) - 3) - 2)/(-3(-2e^(2x) - 3) + 1)) + 1)/(3((-1(-2e^(2x) - 3) - 2)/(-3(-2e^(2x) - 3) + 1)) + 2)))^2 - 2(3((-1((-1(-2e^(2x) - 3) - 2)/(-3(-2e^(2x) - 3) + 1)) + 1)/(3((-1(-2e^(2x) - 3) - 2)/(-3(-2e^(2x) - 3) + 1)) + 2))) - 2 and g(x) = -1(1|(4(1x + 1)^2 - 3(1x + 1) + 3) - 1| - 1) - 2 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = 2(4((-1(4((1x - 1)/(-3x - 1))^2 + 5((1x - 1)/(-3x - 1)) - 3) + 1)/(3(4((1x - 1)/(-3x - 1))^2 + 5((1x - 1)/(-3x - 1)) - 3))) - 4)^2 - 5(4((-1(4((1x - 1)/(-3x - 1))^2 + 5((1x - 1)/(-3x - 1)) - 3) + 1)/(3(4((1x - 1)/(-3x - 1))^2 + 5((1x - 1)/(-3x - 1)) - 3))) - 4) + 4 and g(x) = 2sin(1\u03c0((3(-2(3|x|) + 3) - 2)/(2(-2(3|x|) + 3) + 3)) - 2) + 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -5(3((2(2e^(1(-2|x| + 1)) + 1) - 2)/(-1(2e^(1(-2|x| + 1)) + 1))))^2 - 4(3((2(2e^(1(-2|x| + 1)) + 1) - 2)/(-1(2e^(1(-2|x| + 1)) + 1)))) + 2 and g(x) = 2e^(-1((-2(1(1x + 1)^2 + 3(1x + 1) - 4) + 1)/(2(1(1x + 1)^2 + 3(1x + 1) - 4)))) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-5", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -3|(-3cos(2\u03c0(1|(1(-1x^2 - 1x + 4)^2 + 3(-1x^2 - 1x + 4) - 4) - 1| + 2) + 2) - 1) + 2| + 1 and g(x) = -3(-1((2(-5x - 3) + 3)/(-1(-5x - 3) + 3))^2 - 3)^2 - 4(-1((2(-5x - 3) + 3)/(-1(-5x - 3) + 3))^2 - 3) + 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = (2(1(-1(-2|(-1x^2 - 2x) + 1|)^2 + 5)^2 + 2(-1(-2|(-1x^2 - 2x) + 1|)^2 + 5) - 1) - 1)/(-3(1(-1(-2|(-1x^2 - 2x) + 1|)^2 + 5)^2 + 2(-1(-2|(-1x^2 - 2x) + 1|)^2 + 5) - 1) + 4) and g(x) = -1(-1|(-5((1x - 2)/(3x - 1))^2 - 5((1x - 2)/(3x - 1)) - 3)| - 3)^2 - 3(-1|(-5((1x - 2)/(3x - 1))^2 - 5((1x - 2)/(3x - 1)) - 3)| - 3) + 5 intersect in the range -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = 1(-2(2(-1(2x)^2 - 1(2x) + 5) + 1) + 4) - 2 and g(x) = 1(-2e^(-2((-1(-1|x + 1| + 1))/(2(-1|x + 1| + 1) + 1))))^2 + 1(-2e^(-2((-1(-1|x + 1| + 1))/(2(-1|x + 1| + 1) + 1)))) + 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(2|((1(3(-3x - 1) - 3) - 1)/(-2(3(-3x - 1) - 3) + 1)) + 1| - 3) + 2)/(3(2|((1(3(-3x - 1) - 3) - 1)/(-2(3(-3x - 1) - 3) + 1)) + 1| - 3) + 1) and g(x) = 2((2(-2(-5x + 5) + 5) - 1)/(-2(-2(-5x + 5) + 5) - 3)) - 5 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2cos(1\u03c0(3|((-2((-1(-2|x + 2| + 2) + 3)/(-3(-2|x + 2| + 2) - 1)) + 1)/(2((-1(-2|x + 2| + 2) + 3)/(-3(-2|x + 2| + 2) - 1)) - 1)) + 1|) - 3) + 1 and g(x) = 3(1(-4((-3x - 1)/(2x + 3))^2 - 5((-3x - 1)/(2x + 3)) + 3)^2 + 5(-4((-3x - 1)/(2x + 3))^2 - 5((-3x - 1)/(2x + 3)) + 3) - 4) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-4", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = 2|(-2(-3e^(1((-1(-1x^2 + 1x) - 3)/(-1(-1x^2 + 1x) + 2))) + 3) + 3) + 2| and g(x) = (-2(-3|(2|(-1|x - 2| + 1)| + 1) - 2| - 3) + 3)/(-3(-3|(2|(-1|x - 2| + 1)| + 1) - 2| - 3)) in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = (2(-3|(1(1|(2x - 3)| + 1) - 3)| + 3))/(-2(-3|(1(1|(2x - 3)| + 1) - 3)| + 3) - 3) and g(x) = -3(2|(1(-2|x + 2| - 3) - 1) + 1| + 1)^2 - 3(2|(1(-2|x + 2| - 3) - 1) + 1| + 1) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = 2(5(-4((-3(-1x + 5) + 2)/(3(-1x + 5) + 3))^2 - 1((-3(-1x + 5) + 2)/(3(-1x + 5) + 3)) - 2)^2 + 1(-4((-3(-1x + 5) + 2)/(3(-1x + 5) + 3))^2 - 1((-3(-1x + 5) + 2)/(3(-1x + 5) + 3)) - 2) - 5)^2 - 2(5(-4((-3(-1x + 5) + 2)/(3(-1x + 5) + 3))^2 - 1((-3(-1x + 5) + 2)/(3(-1x + 5) + 3)) - 2)^2 + 1(-4((-3(-1x + 5) + 2)/(3(-1x + 5) + 3))^2 - 1((-3(-1x + 5) + 2)/(3(-1x + 5) + 3)) - 2) - 5) - 2 and g(x) = (1(1|(-3sin(2\u03c0((2x + 3)/(-2x)) + 3) - 3) + 1| - 3) + 3)/(3(1|(-3sin(2\u03c0((2x + 3)/(-2x)) + 3) - 3) + 1| - 3) - 2) meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (-1((3(-4(-2|(-2|x + 2| + 1) + 2| - 1)^2 - 1(-2|(-2|x + 2| + 1) + 2| - 1) + 4) + 1)/(1(-4(-2|(-2|x + 2| + 1) + 2| - 1)^2 - 1(-2|(-2|x + 2| + 1) + 2| - 1) + 4))) - 2)/(-3((3(-4(-2|(-2|x + 2| + 1) + 2| - 1)^2 - 1(-2|(-2|x + 2| + 1) + 2| - 1) + 4) + 1)/(1(-4(-2|(-2|x + 2| + 1) + 2| - 1)^2 - 1(-2|(-2|x + 2| + 1) + 2| - 1) + 4))) + 4) and g(x) = 2|((1((-2(2e^(-1x) - 2) - 2)/(-1(2e^(-1x) - 2) + 2)) - 2)/(1((-2(2e^(-1x) - 2) - 2)/(-1(2e^(-1x) - 2) + 2)) + 3)) - 3| + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -2((-2(2(5((-1x + 2)/(-2x + 3))^2 + 2((-1x + 2)/(-2x + 3))) - 3) - 3)/(-1(2(5((-1x + 2)/(-2x + 3))^2 + 2((-1x + 2)/(-2x + 3))) - 3))) - 5 and g(x) = 2|((-1((-1(-3x - 3) - 3)/(1(-3x - 3) + 3)) + 3)/(-3((-1(-3x - 3) - 3)/(1(-3x - 3) + 3)) + 4)) + 2| - 3 meet in the interval [-10, 10] and round to the nearest integer, what do you get?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 3|((3((-3(-3|((2x - 1)/(-1x)) + 2| + 3) + 1)/(3(-3|((2x - 1)/(-1x)) + 2| + 3) + 1)) - 3)/(-2((-3(-3|((2x - 1)/(-1x)) + 2| + 3) + 1)/(3(-3|((2x - 1)/(-1x)) + 2| + 3) + 1)) + 3))| + 2 and g(x) = 3cos(1\u03c0(2|(-4(1x - 3)^2 - 3(1x - 3) + 3) + 3| - 3) - 1) + 1 meet in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -5((-1(-3sin(2\u03c0((2(1x^2 + 1) - 2)/(-2(1x^2 + 1) - 2)) + 1) + 3) + 1)/(3(-3sin(2\u03c0((2(1x^2 + 1) - 2)/(-2(1x^2 + 1) - 2)) + 1) + 3) + 3))^2 - 5((-1(-3sin(2\u03c0((2(1x^2 + 1) - 2)/(-2(1x^2 + 1) - 2)) + 1) + 3) + 1)/(3(-3sin(2\u03c0((2(1x^2 + 1) - 2)/(-2(1x^2 + 1) - 2)) + 1) + 3) + 3)) - 1 and g(x) = -2(-3((-3((-2x + 2)/(-3x - 2)) - 1)/(-1((-2x + 2)/(-3x - 2)) + 3)) + 4)^2 + 1(-3((-3((-2x + 2)/(-3x - 2)) - 1)/(-1((-2x + 2)/(-3x - 2)) + 3)) + 4) + 4 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -1(3|(-4(-4(5x + 2)^2 + 2(5x + 2) + 3)^2 - 2(-4(5x + 2)^2 + 2(5x + 2) + 3) + 3) - 2| - 2) + 1 and g(x) = 3(2((-2(-2|x + 1| + 2) + 3)/(2(-2|x + 1| + 2) + 2))) + 1 meet in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -1cos(3\u03c0(-1(-2(2|(3x^2 + 1x + 1) + 2| - 2) - 2)) + 1) and g(x) = 3|((-1(2(-4x^2 + 4x + 4) - 3) + 1)/(2(2(-4x^2 + 4x + 4) - 3) - 3)) - 1| - 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the first intersection point (counting from left to right) between the functions f(x) = -2(3|((-3((2((3x + 3)/(-3x - 2)) - 1)/(-3((3x + 3)/(-3x - 2)) + 4)) + 3)/(-1((2((3x + 3)/(-3x - 2)) - 1)/(-3((3x + 3)/(-3x - 2)) + 4)) + 3)) - 2|) - 3 and g(x) = -2|((-2((1(-4x - 5) + 3)/(-3(-4x - 5) - 1)) - 1)/(2((1(-4x - 5) + 3)/(-3(-4x - 5) - 1)) - 1)) - 1| + 3 in the interval [-10, 10], rounded to the nearest integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = -5(-1|(5(1(-3|x + 2| - 3) + 1)^2 - 5(1(-3|x + 2| - 3) + 1) + 2) - 2| + 3)^2 - 1 and g(x) = -1(-1|(3(-4x^2 + 4x) - 3) - 1|)^2 + 4(-1|(3(-4x^2 + 4x) - 3) - 1|) + 3 intersect in the interval [-10, 10].\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-2", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 5(-2sin(3\u03c0((-1((1(-2x - 3))/(-1(-2x - 3) - 3)))/(-1((1(-2x - 3))/(-1(-2x - 3) - 3)) + 2))) - 1) - 4 and g(x) = 2(3|((-2(3x^2 - 5x + 2) + 1)/(2(3x^2 - 5x + 2))) - 1| - 1)^2 + 2(3|((-2(3x^2 - 5x + 2) + 1)/(2(3x^2 - 5x + 2))) - 1| - 1) + 1 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = 1((-1(-4(-2(1|x - 2| + 1)^2 - 1(1|x - 2| + 1) - 2)^2 + 4(-2(1|x - 2| + 1)^2 - 1(1|x - 2| + 1) - 2) + 2) + 2)/(1(-4(-2(1|x - 2| + 1)^2 - 1(1|x - 2| + 1) - 2)^2 + 4(-2(1|x - 2| + 1)^2 - 1(1|x - 2| + 1) - 2) + 2)))^2 + 3((-1(-4(-2(1|x - 2| + 1)^2 - 1(1|x - 2| + 1) - 2)^2 + 4(-2(1|x - 2| + 1)^2 - 1(1|x - 2| + 1) - 2) + 2) + 2)/(1(-4(-2(1|x - 2| + 1)^2 - 1(1|x - 2| + 1) - 2)^2 + 4(-2(1|x - 2| + 1)^2 - 1(1|x - 2| + 1) - 2) + 2))) - 1 and g(x) = (-2(3|((2((-3x + 2)/(3x - 1)) + 1)/(1((-3x + 2)/(3x - 1)))) + 1| - 1) + 2)/(-2(3|((2((-3x + 2)/(3x - 1)) + 1)/(1((-3x + 2)/(3x - 1)))) + 1| - 1) - 3) intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2(-5(1|(4((3x)/(3x - 2)) - 3) + 1| + 3)^2 - 2(1|(4((3x)/(3x - 2)) - 3) + 1| + 3)) - 2 and g(x) = -4(3((-3(-3x + 3))/(-1(-3x + 3) - 3))^2 + 1((-3(-3x + 3))/(-1(-3x + 3) - 3)) - 2) - 2 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"}
{"messages": [{"content": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2|(2(1(-3|((-2x + 2)/(3x + 2)) - 1|) + 5)^2 + 4(1(-3|((-2x + 2)/(3x + 2)) - 1|) + 5) - 2) - 2| - 3 and g(x) = 4((2(5(1x^2 - 3x + 1)) - 1)/(1(5(1x^2 - 3x + 1)) + 2)) + 3 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "3", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (3((2(-1(-2((-2x + 3)/(-1x + 2)) + 2) + 1) - 3)/(-1(-1(-2((-2x + 3)/(-1x + 2)) + 2) + 1))) + 2)/(-1((2(-1(-2((-2x + 3)/(-1x + 2)) + 2) + 1) - 3)/(-1(-1(-2((-2x + 3)/(-1x + 2)) + 2) + 1)))) and g(x) = 2(1|(2|(-4x) + 1| + 3) - 1| + 3)^2 + 1(1|(2|(-4x) + 1| + 3) - 1| + 3) - 5 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(-1(-1((-2(2e^(-1x)) - 1)/(-2(2e^(-1x)) + 3)) + 1)^2 + 5(-1((-2(2e^(-1x)) - 1)/(-2(2e^(-1x)) + 3)) + 1) + 4)^2 + 5(-1(-1((-2(2e^(-1x)) - 1)/(-2(2e^(-1x)) + 3)) + 1)^2 + 5(-1((-2(2e^(-1x)) - 1)/(-2(2e^(-1x)) + 3)) + 1) + 4) + 1 and g(x) = -3(1(2((-3x - 2)/(-3x + 4)) - 1)^2 - 2(2((-3x - 2)/(-3x + 4)) - 1) + 3) + 4 intersect in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "-1", "dataset": "MATH"}