{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = 3(-2sin(3\u03c0(-2|(1x^2 + 2) - 1|)) + 3) + 3 and g(x) = 1|(1((3x - 3)/(3x - 1)) + 5) - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3|(-4((-3x - 3)/(-2x - 2)) - 3) + 3| and g(x) = -1e^(1((2x + 1)/(3x - 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(2x^2 - 2x - 4) - 2)/(1(2x^2 - 2x - 4) + 3)) - 2| + 2 and g(x) = (-1(-1|x + 3| + 2) - 2)/(3(-1|x + 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": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = (-2(5(-2|x - 1| + 2) + 5) + 1)/(1(5(-2|x - 1| + 2) + 5) + 2) and g(x) = 4(1|x + 1| + 3)^2 - 3(1|x + 1| + 3) + 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 leftmost x-coordinate where f(x) = 3((-1(1sin(3\u03c0(-5x + 2) - 2) - 3) + 3)/(3(1sin(3\u03c0(-5x + 2) - 2) - 3) + 3))^2 + 4((-1(1sin(3\u03c0(-5x + 2) - 2) - 3) + 3)/(3(1sin(3\u03c0(-5x + 2) - 2) - 3) + 3)) + 4 and g(x) = (-1(-2|(4x + 2) - 2|) + 3)/(1(-2|(4x + 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 closest to the smallest x-value where the functions f(x) = 3|((-1(1cos(2\u03c0(-3x - 3) - 1)) + 1)/(-2(1cos(2\u03c0(-3x - 3) - 1)) + 1))| - 1 and g(x) = -5(3e^(-2(3|x - 3|)) - 3)^2 - 2(3e^(-2(3|x - 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -4(-2(1|((3x + 1)/(-2x - 2)) + 3|)^2 + 3(1|((3x + 1)/(-2x - 2)) + 3|) + 3) + 3 and g(x) = 4(2|((-3x + 3)/(2x + 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 integer closest to the largest x-value where the functions f(x) = -2(1|(-3((-2x + 3)/(3x + 3)) - 4) + 3| - 2)^2 + 3(1|(-3((-2x + 3)/(3x + 3)) - 4) + 3| - 2) + 5 and g(x) = -2((-1(1|x + 1| - 1) + 2)/(3(1|x + 1| - 1)))^2 - 1((-1(1|x + 1| - 1) + 2)/(3(1|x + 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) = 3|(-1((-2(-2x^2 - 2x + 4))/(-3(-2x^2 - 2x + 4) + 4)) - 5) - 2| - 2 and g(x) = 3e^(-2(4((-2x + 2)/(-2x - 2))^2 + 1((-2x + 2)/(-2x - 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 second intersection point (counting from left to right) between the functions f(x) = -2(4((3(3|x + 2| + 3))/(2(3|x + 2| + 3) - 1))^2 - 5((3(3|x + 2| + 3))/(2(3|x + 2| + 3) - 1)) - 3) - 2 and g(x) = -5((3(2|x + 1| - 3) - 3)/(-2(2|x + 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": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 5(2(-2|((3x - 1)/(-3x + 4)) + 3| - 2)^2 + 2(-2|((3x - 1)/(-3x + 4)) + 3| - 2)) + 2 and g(x) = 3|(-1((2x + 2)/(1x - 2))^2 - 1((2x + 2)/(1x - 2)) + 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": "Find the first intersection point (counting from left to right) between the functions f(x) = -2|(5(-2((-2x + 3)/(-2x))^2 - 1((-2x + 3)/(-2x)) - 4)) - 1| + 3 and g(x) = -1(2|((1x)/(2x - 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": "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|(5x^2 - 1) + 2| + 3) + 4))/(2(1(-1|(5x^2 - 1) + 2| + 3) + 4) - 1) and g(x) = -2|((3(-1x + 4))/(-1(-1x + 4) + 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(-1|(1((2x - 2)/(-2x - 3)) + 1) - 3| + 3)^2 - 2(-1|(1((2x - 2)/(-2x - 3)) + 1) - 3| + 3) + 2 and g(x) = -1e^(1(4(-2x^2 + 2x + 1) - 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": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = -2((1(1|(1x - 1) - 2| - 2) - 3)/(-1(1|(1x - 1) - 2| - 2) - 3))^2 - 4((1(1|(1x - 1) - 2| - 2) - 3)/(-1(1|(1x - 1) - 2| - 2) - 3)) and g(x) = -1(-2|(1x - 5) + 3|)^2 + 3(-2|(1x - 5) + 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": "At what integer value (rounded) do the functions f(x) = -5(3|((-1(4x + 1) + 1)/(1(4x + 1))) + 2| + 1)^2 - 3(3|((-1(4x + 1) + 1)/(1(4x + 1))) + 2| + 1) + 2 and g(x) = -1e^(-2(-3((-3x + 3)/(1x - 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 value closest to the x-coordinate where f(x) = 1|((-1(5(2x^2 + 5x - 3) - 1) - 3)/(2(5(2x^2 + 5x - 3) - 1) - 3)) + 1| + 2 and g(x) = -2e^(2(-4(3x^2 + 1x + 5) + 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) = -4(-3e^(2((-3(1|x - 3| - 2) - 1)/(-2(1|x - 3| - 2))))) - 2 and g(x) = (2(-1(-5x + 1)^2 - 4(-5x + 1) - 3) - 3)/(3(-1(-5x + 1)^2 - 4(-5x + 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 rightmost x-coordinate where f(x) = -3(-4(3e^(2((-1x - 3)/(1x + 2))) + 3)^2 + 3(3e^(2((-1x - 3)/(1x + 2))) + 3) + 5) - 4 and g(x) = (-2(-1(3|x - 1| - 1)^2 + 2(3|x - 1| - 1) + 4) + 3)/(-2(-1(3|x - 1| - 1)^2 + 2(3|x - 1| - 1) + 4) + 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(1|(2(2e^(-1x)) + 4) - 3| - 2)^2 - 3(1|(2(2e^(-1x)) + 4) - 3| - 2) + 3 and g(x) = (1(1e^(-1(-1|x - 2| - 3)) + 1) + 3)/(-2(1e^(-1(-1|x - 2| - 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": "Find the integer closest to the largest x-value where the functions f(x) = (2(-2|(2x^2 - 4x - 3)| - 1) - 3)/(3(-2|(2x^2 - 4x - 3)| - 1) + 3) and g(x) = -1((2x - 2)/(-1x + 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) = 1|((1(-1sin(2\u03c0x - 1) - 3) - 2)/(-2(-1sin(2\u03c0x - 1) - 3) - 2)) + 1| + 1 and g(x) = -5(-3e^(-1x) + 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 closest to the largest x-value where the functions f(x) = -1(-4((-3x - 2)/(-1x - 1))^2 + 5) + 4 and g(x) = 1|(2e^(-1x) + 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (-3(-1cos(3\u03c0(2x^2 - 2) + 1) + 2) - 3)/(1(-1cos(3\u03c0(2x^2 - 2) + 1) + 2)) and g(x) = (3(-4x^2 - 2x + 1) - 3)/(-3(-4x^2 - 2x + 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": "At what integer value (rounded) do the functions f(x) = -1(1|(-1cos(3\u03c0((-1x)/(2x + 3)) + 1)) + 2| + 1)^2 - 2(1|(-1cos(3\u03c0((-1x)/(2x + 3)) + 1)) + 2| + 1) - 4 and g(x) = (2(-2(-2e^(2x) + 3)^2 - 5(-2e^(2x) + 3) + 1) - 3)/(-3(-2(-2e^(2x) + 3)^2 - 5(-2e^(2x) + 3) + 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": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -2(-1|((2x + 3)/(-3x)) + 2| + 1)^2 + 1(-1|((2x + 3)/(-3x)) + 2| + 1) + 3 and g(x) = 2|((-2x - 3)/(3x - 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": "If you add up all the x-coordinates where the functions f(x) = 1(3|(3((-3x - 2)/(-1x + 2)) - 1) + 3| + 3)^2 + 4(3|(3((-3x - 2)/(-1x + 2)) - 1) + 3| + 3) - 4 and g(x) = 5(2(-3|x - 3| + 1) - 3)^2 - 2(2(-3|x - 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": "8", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -1(-5((-2(-2|x + 1| + 3))/(3(-2|x + 1| + 3)))^2 + 1((-2(-2|x + 1| + 3))/(3(-2|x + 1| + 3))) + 3) + 2 and g(x) = 1|(2(5x^2 - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 1((-1(3(2|x| - 2)^2 + 4(2|x| - 2) + 4))/(3(3(2|x| - 2)^2 + 4(2|x| - 2) + 4) - 2)) - 1 and g(x) = -5(4((2x)/(-3x - 1)) + 5)^2 - 2(4((2x)/(-3x - 1)) + 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1e^(2((1(3(-5x + 2)^2 - 3(-5x + 2) - 3) + 1)/(-1(3(-5x + 2)^2 - 3(-5x + 2) - 3) - 2))) + 1 and g(x) = 4(3e^(2(2|x - 3| - 1)) - 3) + 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 average of all x-coordinates (rounded to the nearest integer) where f(x) = (1(1(1(-1|x| - 2)^2 + 1(-1|x| - 2) + 2) + 5) - 2)/(-1(1(1(-1|x| - 2)^2 + 1(-1|x| - 2) + 2) + 5)) and g(x) = -5(-1(-2|x + 2| - 1)^2 - 4(-2|x + 2| - 1) + 5) - 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 sum of all x-coordinates (rounded to the nearest integer) where f(x) = 1(3|(3((-2x + 1)/(2x + 2)) + 4)|)^2 - 1(3|(3((-2x + 1)/(2x + 2)) + 4)|) + 5 and g(x) = 1(1|((-3x - 3)/(-3x - 1)) + 2| - 1)^2 + 3(1|((-3x - 3)/(-3x - 1)) + 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": "Find the integer closest to the smallest x-value where the functions f(x) = -1e^(1(-1((3(1x^2 - 1x - 2))/(2(1x^2 - 1x - 2) - 1)) - 5)) + 1 and g(x) = 1cos(3\u03c0(-4(3|x + 1| - 3)^2 + 4(3|x + 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": "-1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer value closest to the x-coordinate where f(x) = -5(2|((-2x)/(-3x))| - 3)^2 + 1(2|((-2x)/(-3x))| - 3) - 1 and g(x) = (-2(5x - 3) - 1)/(3(5x - 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": "1", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the smallest x-value where the functions f(x) = 1(-2|((-2(-5x + 4) - 1)/(3(-5x + 4) - 1)) - 1|)^2 + 5(-2|((-2(-5x + 4) - 1)/(3(-5x + 4) - 1)) - 1|) - 4 and g(x) = 2(3sin(3\u03c0((1x + 2)/(2x + 1)) - 3) + 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(1cos(1\u03c0x - 3) - 1) + 2)/(3(1cos(1\u03c0x - 3) - 1))) + 3| - 3 and g(x) = (-3(-2x + 2) + 2)/(-2(-2x + 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(-4(3(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) + 1) + 1) - 2)/(1(-4(3(2|x - 1| - 2)^2 - 5(2|x - 1| - 2) + 1) + 1)) and g(x) = 4(-2|(-4x + 1) - 1|)^2 - 2(-2|(-4x + 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) = 3|(1cos(2\u03c0(2(1x^2 + 2x) + 5) + 1) + 2) - 1| + 3 and g(x) = (-1(3(-1e^(2x) + 2) + 5) + 2)/(-3(3(-1e^(2x) + 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 2(-1cos(3\u03c0((2(-1x) + 3)/(2(-1x) + 3)) + 2) - 3)^2 + 2(-1cos(3\u03c0((2(-1x) + 3)/(2(-1x) + 3)) + 2) - 3) - 3 and g(x) = (-3(-3|(1x^2 + 4x + 4)| + 1) - 3)/(2(-3|(1x^2 + 4x + 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": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 2((3(3e^(-1(-4x^2 - 1x + 2)) - 1) + 1)/(1(3e^(-1(-4x^2 - 1x + 2)) - 1) - 2)) - 2 and g(x) = 2((-2(1|x + 1| - 3))/(-1(1|x + 1| - 3) + 3))^2 - 3((-2(1|x + 1| - 3))/(-1(1|x + 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 rightmost x-coordinate where f(x) = (-3(1|(5x + 3) - 2| - 3) - 3)/(3(1|(5x + 3) - 2| - 3) + 2) and g(x) = 3(-3e^(-1x) + 2)^2 + 1(-3e^(-1x) + 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": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (3(2sin(3\u03c0(3|(5x^2 - 2x + 5) - 3| - 2) + 3) + 2))/(-3(2sin(3\u03c0(3|(5x^2 - 2x + 5) - 3| - 2) + 3) + 2) - 1) and g(x) = -3(-4((3x - 2)/(1x)) + 2)^2 - 4(-4((3x - 2)/(1x)) + 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 second x-coordinate (rounded to the nearest integer) where f(x) = -3sin(2\u03c0((1(-1(1|x - 1| + 2)^2 - 2(1|x - 1| + 2) + 4) + 3)/(-3(-1(1|x - 1| + 2)^2 - 2(1|x - 1| + 2) + 4) + 4)) - 2) + 1 and g(x) = -2sin(1\u03c0((-3(-3|x + 1|) + 2)/(-3(-3|x + 1|) - 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = 5(5(1|((-1x - 1)/(2x - 3)) + 1| - 1) + 4)^2 + 1(5(1|((-1x - 1)/(2x - 3)) + 1| - 1) + 4) - 2 and g(x) = -4(-3|(4x^2 + 1x + 5) - 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 first intersection point (counting from left to right) between the functions f(x) = (-1(-2|(5(1e^(2x))^2 - 5(1e^(2x)) - 5) - 3|) - 3)/(-3(-2|(5(1e^(2x))^2 - 5(1e^(2x)) - 5) - 3|) - 1) and g(x) = (2(-1(3e^(2x) - 2) + 3) - 1)/(-1(-1(3e^(2x) - 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": "0", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = 2(2sin(2\u03c0(1|((-1x)/(2x - 1)) + 2| - 3)) - 2)^2 + 5(2sin(2\u03c0(1|((-1x)/(2x - 1)) + 2| - 3)) - 2) + 3 and g(x) = 2(5((-1x - 2)/(3x + 2))^2 + 3((-1x - 2)/(3x + 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -1(5(2e^(1(2|x - 3| - 2)))^2 + 4(2e^(1(2|x - 3| - 2))) + 5) - 3 and g(x) = -3(3e^(-1((2x + 1)/(-1x - 2))) - 1)^2 - 1(3e^(-1((2x + 1)/(-1x - 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 average of all x-coordinates (rounded to the nearest integer) where f(x) = 2(4((-1(1e^(1x) - 2) + 3)/(-2(1e^(1x) - 2) - 3))^2 + 4((-1(1e^(1x) - 2) + 3)/(-2(1e^(1x) - 2) - 3)) - 5) + 5 and g(x) = 3(-1(3|x + 1|) + 5)^2 - 1(-1(3|x + 1|) + 5) + 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2((-2(1cos(3\u03c0x + 2) + 2) - 3)/(1(1cos(3\u03c0x + 2) + 2) + 2))^2 + 1((-2(1cos(3\u03c0x + 2) + 2) - 3)/(1(1cos(3\u03c0x + 2) + 2) + 2)) + 4 and g(x) = (1(2x^2 + 4x - 4))/(2(2x^2 + 4x - 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": "If you add up all the x-coordinates where the functions f(x) = -2|((-2(-4(-4x)^2 - 1(-4x)) + 1)/(1(-4(-4x)^2 - 1(-4x)) - 2)) - 1| - 3 and g(x) = -2(3|((2x)/(3x + 3)) - 3| + 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": "-3", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = 3(-3|(-4x^2 + 1x + 3)|) + 4 and g(x) = 2|((3x - 3)/(2x + 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": "If you add up all the x-coordinates where the functions f(x) = -1(1|(4((-2x)/(2x - 1))^2 + 3((-2x)/(2x - 1))) + 1| - 3) + 3 and g(x) = 2(-5(3|x - 1| - 3)^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": "1", "dataset": "MATH"}
{"messages": [{"content": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = -3|(-1(5x^2 + 4x + 1) - 2) + 3| - 2 and g(x) = -3|(-1cos(1\u03c0x + 2) + 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) = 5((-2(-1|(2x + 1) - 3| + 2) + 1)/(2(-1|(2x + 1) - 3| + 2) + 2))^2 - 1((-2(-1|(2x + 1) - 3| + 2) + 1)/(2(-1|(2x + 1) - 3| + 2) + 2)) - 2 and g(x) = 1((1(-1sin(1\u03c0x - 3) - 2) + 2)/(-3(-1sin(1\u03c0x - 3) - 2) + 4)) + 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": "-9", "dataset": "MATH"}
{"messages": [{"content": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(-1(2cos(3\u03c0x - 1) + 2)^2 - 5(2cos(3\u03c0x - 1) + 2) - 2) + 2)/(-2(-1(2cos(3\u03c0x - 1) + 2)^2 - 5(2cos(3\u03c0x - 1) + 2) - 2) + 3) and g(x) = -5(1x^2 - 2x + 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": "When ordered from left to right, what is the first x-coordinate (rounded to the nearest integer) where f(x) = -3|((1(-5(5x^2 - 2x - 1) + 3) + 3)/(2(-5(5x^2 - 2x - 1) + 3) + 2)) - 3| + 3 and g(x) = 4((3(-5x^2 - 4x - 1) - 2)/(2(-5x^2 - 4x - 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": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 2((-2(-2|(2x - 1) - 2| - 3) - 1)/(1(-2|(2x - 1) - 2| - 3)))^2 + 1((-2(-2|(2x - 1) - 2| - 3) - 1)/(1(-2|(2x - 1) - 2| - 3))) + 5 and g(x) = -1(-5(2|x| - 2)^2 - 5(2|x| - 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = (2(5(-3|(1x - 5) - 2|)^2 + 5(-3|(1x - 5) - 2|) - 1) - 3)/(-3(5(-3|(1x - 5) - 2|)^2 + 5(-3|(1x - 5) - 2|) - 1) - 1) and g(x) = 5((2(-1sin(3\u03c0x - 2) - 3) + 3)/(-2(-1sin(3\u03c0x - 2) - 3) - 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": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -3((2(-1(-2e^(2x) + 2)^2 + 3(-2e^(2x) + 2) + 1) - 1)/(-1(-1(-2e^(2x) + 2)^2 + 3(-2e^(2x) + 2) + 1) - 1)) + 4 and g(x) = -3|((3(-4x^2 - 4x - 5))/(2(-4x^2 - 4x - 5) + 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) = -3(2(-3|((2x - 3)/(2x + 2)) - 2| + 2) + 2)^2 - 4(2(-3|((2x - 3)/(2x + 2)) - 2| + 2) + 2) and g(x) = -1(3|((3x)/(1x - 2)) + 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": "Round to the nearest integer: what is the x-coordinate where the graphs of f(x) = -1|((3(-5(-2cos(2\u03c0x + 3) - 3)^2 + 1(-2cos(2\u03c0x + 3) - 3) - 2) - 1)/(-3(-5(-2cos(2\u03c0x + 3) - 3)^2 + 1(-2cos(2\u03c0x + 3) - 3) - 2) - 3)) - 2| - 1 and g(x) = 1(-2((1x - 1)/(-1x + 2)) - 2)^2 + 2(-2((1x - 1)/(-1x + 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) = (-1(5(-2(-1sin(3\u03c0x - 2) - 2)^2 + 3(-1sin(3\u03c0x - 2) - 2) + 1) + 4) + 2)/(3(5(-2(-1sin(3\u03c0x - 2) - 2)^2 + 3(-1sin(3\u03c0x - 2) - 2) + 1) + 4) - 1) and g(x) = (2(-1(1x^2 - 4x - 5) + 4) - 1)/(3(-1(1x^2 - 4x - 5) + 4) + 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 sum of all x-coordinates (rounded to the nearest integer) where f(x) = -4(-1((2(-2|x + 2| - 2) - 2)/(3(-2|x + 2| - 2) + 3)) - 2)^2 + 4(-1((2(-2|x + 2| - 2) - 2)/(3(-2|x + 2| - 2) + 3)) - 2) - 5 and g(x) = -2|(-1(5x^2 - 5x - 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": "When ordered from left to right, what is the second x-coordinate (rounded to the nearest integer) where f(x) = (-1(1sin(3\u03c0(-3x^2 + 3x)) + 2) - 3)/(-1(1sin(3\u03c0(-3x^2 + 3x)) + 2) - 1) and g(x) = -1((2x + 3)/(1x + 1))^2 - 5((2x + 3)/(1x + 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": "If you add up all the x-coordinates where the functions f(x) = 1e^(-1((1(1(-1|x + 3| - 1) - 1) - 3)/(2(1(-1|x + 3| - 1) - 1) - 1))) + 3 and g(x) = 1|(-5(1x + 2)^2 - 3(1x + 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": "-5", "dataset": "MATH"}
{"messages": [{"content": "If you add up all the x-coordinates where the functions f(x) = -5(-3((3(3sin(1\u03c0x - 1)) - 2)/(-2(3sin(1\u03c0x - 1)) - 1)) - 1)^2 + 1 and g(x) = 3|(3(-2x^2 - 5x + 1) + 4) - 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": "Find the integer closest to the largest x-value where the functions f(x) = -2((1(-2x))/(-1(-2x) - 1))^2 + 5((1(-2x))/(-1(-2x) - 1)) + 3 and g(x) = (2(2x^2 + 2x - 2) + 1)/(1(2x^2 + 2x - 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(-1cos(2\u03c0x - 2) + 2) + 1)/(-3(-1cos(2\u03c0x - 2) + 2) + 2))^2 - 1((2(-1cos(2\u03c0x - 2) + 2) + 1)/(-3(-1cos(2\u03c0x - 2) + 2) + 2)) + 1 and g(x) = 1(-5x + 2)^2 - 1(-5x + 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) = -3(1|(1e^(2((-2x + 2)/(-1x + 2))) - 3) + 1| - 3) + 3 and g(x) = -3(5(-2|x + 2|) + 1)^2 - 1(5(-2|x + 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) = 3|((-3(-4(5x^2 + 5x - 5) - 4) - 3)/(-2(-4(5x^2 + 5x - 5) - 4) - 3)) + 3| + 1 and g(x) = 1(3e^(2(2x - 4)) - 1)^2 + 2(3e^(2(2x - 4)) - 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": "At what integer value (rounded) do the functions f(x) = 1((-2(-3|x + 2|) - 1)/(-3(-3|x + 2|) + 1))^2 - 1((-2(-3|x + 2|) - 1)/(-3(-3|x + 2|) + 1)) - 1 and g(x) = 1sin(2\u03c0((-3x + 1)/(2x + 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -2|((1(2x^2 + 5x - 5) + 1)/(-2(2x^2 + 5x - 5) - 3)) - 2| - 1 and g(x) = -4(-1e^(1x) + 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 integer closest to the largest x-value where the functions f(x) = 3(2e^(1(-1|x + 3| - 1)) + 1)^2 - 3(2e^(1(-1|x + 3| - 1)) + 1) and g(x) = 1((-1x + 3)/(-1x))^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) = -2|((3(4(1x^2 + 3x + 3) + 4) - 2)/(1(4(1x^2 + 3x + 3) + 4))) + 2| + 3 and g(x) = -3e^(-1((1(2x - 5) + 2)/(3(2x - 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": "3", "dataset": "MATH"}
{"messages": [{"content": "Find the integer closest to the largest x-value where the functions f(x) = -3(3e^(2(-5((3x)/(-2x + 3)) - 3)) - 3)^2 - 5(3e^(2(-5((3x)/(-2x + 3)) - 3)) - 3) + 5 and g(x) = 3sin(3\u03c0(-3(1|x - 2| - 1) + 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 second intersection point (counting from left to right) between the functions f(x) = 1(3e^(-2((-1(-1x + 2) + 1)/(2(-1x + 2) - 1))))^2 + 5(3e^(-2((-1(-1x + 2) + 1)/(2(-1x + 2) - 1)))) + 4 and g(x) = 2|(-1(2x^2 + 5) + 5) - 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": "Find the integer closest to the largest x-value where the functions f(x) = -1|(1((2(-4x - 4) + 1)/(1(-4x - 4) - 2))^2 + 4((2(-4x - 4) + 1)/(1(-4x - 4) - 2)) - 4) - 2| and g(x) = -3e^(1(1|(-4x^2 - 4x - 4) - 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 leftmost x-coordinate where f(x) = -4((-1(-1(-1|x - 1| - 2) - 5) - 2)/(3(-1(-1|x - 1| - 2) - 5) + 2))^2 + 5((-1(-1(-1|x - 1| - 2) - 5) - 2)/(3(-1(-1|x - 1| - 2) - 5) + 2)) - 1 and g(x) = (-3(1|(4x + 3) + 1| + 2) + 2)/(1(1|(4x + 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|(3(5x + 4)^2 + 5(5x + 4) + 5) - 1| and g(x) = 3|((3x + 3)/(1x + 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": "If you add up all the x-coordinates where the functions f(x) = 3(3e^(2(3|((2x - 1)/(1x + 3)) - 1| - 2)) - 2)^2 - 4(3e^(2(3|((2x - 1)/(1x + 3)) - 1| - 2)) - 2) - 5 and g(x) = 3e^(-1((2(2|x + 3| + 1) - 3)/(-2(2|x + 3| + 1) + 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": "10", "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|(3x - 2) + 1| + 2)^2 + 3(-3|(3x - 2) + 1| + 2) + 2) + 3)/(1(2(-3|(3x - 2) + 1| + 2)^2 + 3(-3|(3x - 2) + 1| + 2) + 2) - 2) and g(x) = -2|((-2(-3x^2 - 2x + 1) + 3)/(-1(-3x^2 - 2x + 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": "Round to the nearest integer: what is the leftmost x-coordinate where f(x) = -5(1|(-3cos(3\u03c0x + 2) - 3) - 1| + 1)^2 - 5(1|(-3cos(3\u03c0x + 2) - 3) - 1| + 1) - 4 and g(x) = 2(-1e^(-2x) - 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": "If you add up all the x-coordinates where the functions f(x) = -5((-1(1sin(1\u03c0(-3|x - 1| + 1) + 3) - 3) + 1)/(-1(1sin(1\u03c0(-3|x - 1| + 1) + 3) - 3) - 3))^2 + 5((-1(1sin(1\u03c0(-3|x - 1| + 1) + 3) - 3) + 1)/(-1(1sin(1\u03c0(-3|x - 1| + 1) + 3) - 3) - 3)) + 3 and g(x) = (-2(-1|(1x + 3) - 2| + 2) + 2)/(-2(-1|(1x + 3) - 2| + 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": "-2", "dataset": "MATH"}
{"messages": [{"content": "At what integer value (rounded) do the functions f(x) = (2(-2|(1(-2e^(-1x) + 1)^2 + 2(-2e^(-1x) + 1) + 4) - 2| + 2) - 2)/(2(-2|(1(-2e^(-1x) + 1)^2 + 2(-2e^(-1x) + 1) + 4) - 2| + 2) + 1) and g(x) = 1(-3(3sin(2\u03c0x - 1) - 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) = -4(3|(3sin(2\u03c0((3x - 1)/(-3x - 1)) - 3) - 2) + 2| - 2) + 1 and g(x) = -3|(-5(-4x - 5)^2 - 3(-4x - 5) - 5) + 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": "Round to the nearest integer: what is the rightmost x-coordinate where f(x) = 4(1|(-1((-1x - 2)/(-3x + 4)) + 3) - 3| + 2)^2 - 4(1|(-1((-1x - 2)/(-3x + 4)) + 3) - 3| + 2) - 1 and g(x) = 4(-1|(2e^(1x) - 1) - 3| - 2)^2 + 3(-1|(2e^(1x) - 1) - 3| - 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": "Find the second intersection point (counting from left to right) between the functions f(x) = 3|((-3(2(1sin(3\u03c0x) - 2) - 3) - 2)/(-2(2(1sin(3\u03c0x) - 2) - 3) + 1)) + 3| - 1 and g(x) = 2|(-4(2e^(1x) - 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 leftmost x-coordinate where f(x) = 3((-2(2(1|x - 2| + 3) - 3) + 2)/(2(2(1|x - 2| + 3) - 3)))^2 - 4((-2(2(1|x - 2| + 3) - 3) + 2)/(2(2(1|x - 2| + 3) - 3))) - 2 and g(x) = (2(3(-1x + 1)^2 - 1(-1x + 1) - 1) + 1)/(-2(3(-1x + 1)^2 - 1(-1x + 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 sum of all x-coordinates (rounded to the nearest integer) where f(x) = -5(3|(2(2sin(2\u03c0x + 3) + 2) + 4) - 2|)^2 - 5(3|(2(2sin(2\u03c0x + 3) + 2) + 4) - 2|) + 1 and g(x) = -2e^(-2(-3(1|x + 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -3|(2(3((-1x + 1)/(-3x + 2))^2 - 4((-1x + 1)/(-3x + 2)) - 2) - 3)| and g(x) = (1(2|(5x^2 - 1x + 3) + 2| + 1) - 1)/(-3(2|(5x^2 - 1x + 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": "Find the average of all x-coordinates (rounded to the nearest integer) where f(x) = (-2(1(-1|(3x + 1)| - 1)^2 + 5(-1|(3x + 1)| - 1) - 5) - 2)/(3(1(-1|(3x + 1)| - 1)^2 + 5(-1|(3x + 1)| - 1) - 5) - 1) and g(x) = -3e^(-2(-3(-3|x - 1| + 1) + 4)) + 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) = (2(4(-2cos(3\u03c0x + 2) + 2)^2 + 5(-2cos(3\u03c0x + 2) + 2) + 1))/(1(4(-2cos(3\u03c0x + 2) + 2)^2 + 5(-2cos(3\u03c0x + 2) + 2) + 1) + 2) and g(x) = 3|(-1x + 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 sum of all x-coordinates (rounded to the nearest integer) where f(x) = 3(2((-2x - 3)/(3x)) + 2)^2 - 5(2((-2x - 3)/(3x)) + 2) - 5 and g(x) = 3|((-1x - 1)/(2x + 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(1(1|(-2x - 3) - 1| - 1)^2 + 1(1|(-2x - 3) - 1| - 1) - 3) - 3)/(1(1(1|(-2x - 3) - 1| - 1)^2 + 1(1|(-2x - 3) - 1| - 1) - 3) - 3) and g(x) = (1(2|(-3cos(1\u03c0x + 3) - 3) - 2| - 2) - 2)/(-1(2|(-3cos(1\u03c0x + 3) - 3) - 2| - 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(-3|(-5x - 3) + 1| - 2) - 3)/(2(-3|(-5x - 3) + 1| - 2) - 1))^2 - 1((3(-3|(-5x - 3) + 1| - 2) - 3)/(2(-3|(-5x - 3) + 1| - 2) - 1)) + 1 and g(x) = -3e^(-2((2(5x - 3) - 1)/(2(5x - 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": "What is the mean value of the x-coordinates (rounded to the nearest integer) where the functions f(x) = -5(-3|((-2x + 1)/(2x - 3))|) + 1 and g(x) = 2sin(1\u03c0(1|x - 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) = -3(1|((3x + 2)/(-1x - 2)) + 3| - 3)^2 + 1(1|((3x + 2)/(-1x - 2)) + 3| - 3) - 5 and g(x) = 5(-1e^(-1x) + 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": "Find the integer closest to the largest x-value where the functions f(x) = -4((1(3(3|x + 1|)^2 + 3(3|x + 1|)) - 2)/(-2(3(3|x + 1|)^2 + 3(3|x + 1|)))) + 1 and g(x) = -2((1(1x + 1) - 1)/(-3(1x + 1)))^2 + 1((1(1x + 1) - 1)/(-3(1x + 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": "Find the integer closest to the smallest x-value where the functions f(x) = 3|(-2((-2(5x + 1) - 1)/(2(5x + 1) - 3))^2 + 5((-2(5x + 1) - 1)/(2(5x + 1) - 3)) - 1) + 1| and g(x) = (1(-1(-2sin(1\u03c0x + 1) - 3)^2 - 2(-2sin(1\u03c0x + 1) - 3) + 3) - 1)/(-2(-1(-2sin(1\u03c0x + 1) - 3)^2 - 2(-2sin(1\u03c0x + 1) - 3) + 3) + 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 sum of all x-coordinates (rounded to the nearest integer) where f(x) = -1|((-3(-4x + 4) + 2)/(-2(-4x + 4) - 1)) + 3| - 1 and g(x) = 1((3x)/(1x + 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"}