{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-2(-3sin(1\u03c0((1((2x - 3)/(2x + 2)) - 3)/(1((2x - 3)/(2x + 2)))) - 3) - 2) + 3) - 3)/(1(-2(-3sin(1\u03c0((1((2x - 3)/(2x + 2)) - 3)/(1((2x - 3)/(2x + 2)))) - 3) - 2) + 3) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(4(5(5(-2sin(2\u03c0x - 1) - 2) - 1)^2 + 5(5(-2sin(2\u03c0x - 1) - 2) - 1) - 4)^2 + 5(5(5(-2sin(2\u03c0x - 1) - 2) - 1)^2 + 5(5(-2sin(2\u03c0x - 1) - 2) - 1) - 4) - 3) + 2)/(-2(4(5(5(-2sin(2\u03c0x - 1) - 2) - 1)^2 + 5(5(-2sin(2\u03c0x - 1) - 2) - 1) - 4)^2 + 5(5(5(-2sin(2\u03c0x - 1) - 2) - 1)^2 + 5(5(-2sin(2\u03c0x - 1) - 2) - 1) - 4) - 3) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2|(-2(-1|(-1|x - 2|) + 1| - 1) - 4) + 2| - 1) + 2)/(1(2|(-2(-1|(-1|x - 2|) + 1| - 1) - 4) + 2| - 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(1(2(-5((2x)/(-1x - 2)) - 1)^2 - 4(-5((2x)/(-1x - 2)) - 1) - 4)^2 + 2(2(-5((2x)/(-1x - 2)) - 1)^2 - 4(-5((2x)/(-1x - 2)) - 1) - 4) - 4) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(3((1(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1) + 2)/(-1(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1)))^2 + 2((1(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1) + 2)/(-1(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1)))) + 1)/(3(3((1(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1) + 2)/(-1(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1)))^2 + 2((1(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1) + 2)/(-1(-1|(3sin(1\u03c0x - 1) + 2) - 3| + 1)))) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1|(-3|(1(1cos(3\u03c0x + 2) - 2) + 5) - 3|)| - 1) + 2)/(-1(1|(-3|(1(1cos(3\u03c0x + 2) - 2) + 5) - 3|)| - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-5((-3(4(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2) + 1) - 2)/(2(4(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2) + 1) + 2))^2 - 4((-3(4(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2) + 1) - 2)/(2(4(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2) + 1) + 2)) + 3))/(2(-5((-3(4(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2) + 1) - 2)/(2(4(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2) + 1) + 2))^2 - 4((-3(4(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2) + 1) - 2)/(2(4(-3sin(1\u03c0x + 3) - 2)^2 + 5(-3sin(1\u03c0x + 3) - 2) + 1) + 2)) + 3) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-5(-3sin(2\u03c0(2|((-1x + 1)/(1x + 3)) - 3| - 1) + 3) + 2) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-3(3(3cos(2\u03c0((-3x)/(-3x + 4)) + 2) - 3) + 5)^2 - 5(3(3cos(2\u03c0((-3x)/(-3x + 4)) + 2) - 3) + 5) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(2(-4(-4((2x + 3)/(1x + 3)) - 1)^2 - 3(-4((2x + 3)/(1x + 3)) - 1) - 1)^2 + 3(-4(-4((2x + 3)/(1x + 3)) - 1)^2 - 3(-4((2x + 3)/(1x + 3)) - 1) - 1) - 3) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "660", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-4((2(-2(-2cos(1\u03c0x - 3) - 1)^2 - 3(-2cos(1\u03c0x - 3) - 1) + 3) + 1)/(1(-2(-2cos(1\u03c0x - 3) - 1)^2 - 3(-2cos(1\u03c0x - 3) - 1) + 3)))^2 - 1((2(-2(-2cos(1\u03c0x - 3) - 1)^2 - 3(-2cos(1\u03c0x - 3) - 1) + 3) + 1)/(1(-2(-2cos(1\u03c0x - 3) - 1)^2 - 3(-2cos(1\u03c0x - 3) - 1) + 3))) - 2) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(5(1(3((-3x + 1)/(1x + 1))^2 + 3((-3x + 1)/(1x + 1)) - 5)^2 + 2(3((-3x + 1)/(1x + 1))^2 + 3((-3x + 1)/(1x + 1)) - 5) - 5) + 1)^2 - 5(5(1(3((-3x + 1)/(1x + 1))^2 + 3((-3x + 1)/(1x + 1)) - 5)^2 + 2(3((-3x + 1)/(1x + 1))^2 + 3((-3x + 1)/(1x + 1)) - 5) - 5) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2((-3(1(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2)^2 - 4(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2) + 1))/(1(1(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2)^2 - 4(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2) + 1) + 3)) + 1)/(-1((-3(1(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2)^2 - 4(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2) + 1))/(1(1(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2)^2 - 4(-3(2|x| - 1)^2 + 2(2|x| - 1) + 2) + 1) + 3)) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1(4((-2(-2cos(3\u03c0x) - 1) + 2)/(3(-2cos(3\u03c0x) - 1) - 1)) + 1)^2 + 5(4((-2(-2cos(3\u03c0x) - 1) + 2)/(3(-2cos(3\u03c0x) - 1) - 1)) + 1) - 5) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2((-2(1|(-3(-1x^2 - 3x + 5)) + 2| - 3) + 3)/(-2(1|(-3(-1x^2 - 3x + 5)) + 2| - 3) - 2)) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(4(-2(1|(-3|x - 2| + 3) + 1| + 2)^2 + 4(1|(-3|x - 2| + 3) + 1| + 2) + 1) + 5)| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((-1(-4(2((-1x - 2)/(-2x - 1))^2 - 2((-1x - 2)/(-2x - 1)) - 3) - 5))/(3(-4(2((-1x - 2)/(-2x - 1))^2 - 2((-1x - 2)/(-2x - 1)) - 3) - 5) + 1))^2 - 2((-1(-4(2((-1x - 2)/(-2x - 1))^2 - 2((-1x - 2)/(-2x - 1)) - 3) - 5))/(3(-4(2((-1x - 2)/(-2x - 1))^2 - 2((-1x - 2)/(-2x - 1)) - 3) - 5) + 1)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(3(-1|(4(-3cos(1\u03c0x - 1) + 1)^2 - 4(-3cos(1\u03c0x - 1) + 1))| + 2)^2 + 3(-1|(4(-3cos(1\u03c0x - 1) + 1)^2 - 4(-3cos(1\u03c0x - 1) + 1))| + 2) + 2) - 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((-2((-2(-2|(5x^2 - 4x - 3)| - 1) - 3)/(-1(-2|(5x^2 - 4x - 3)| - 1))))/(3((-2(-2|(5x^2 - 4x - 3)| - 1) - 3)/(-1(-2|(5x^2 - 4x - 3)| - 1))) - 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-3|(-1(2|(-1x^2 - 2x) + 3|)^2 + 3(2|(-1x^2 - 2x) + 3|) - 2) + 1|) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(5(-2(-2sin(2\u03c0(-2x) + 1) + 3)^2 + 2(-2sin(2\u03c0(-2x) + 1) + 3) + 3) + 5) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(3(5(-3(2|x - 1|) + 3) - 5)^2 - 5(5(-3(2|x - 1|) + 3) - 5) - 4) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(1\u03c0(-2((-1(1|(1x^2 + 4)| - 1) - 1)/(-1(1|(1x^2 + 4)| - 1) + 2)) + 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(2cos(3\u03c0(-3|((-1(5x + 5) - 2)/(2(5x + 5) + 1)) - 1| + 2)) + 3)^2 - 4(2cos(3\u03c0(-3|((-1(5x + 5) - 2)/(2(5x + 5) + 1)) - 1| + 2)) + 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(4(4(1|(2|x - 3|) - 2| - 1) + 1) + 1) + 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(-1(3(3|(-4x^2 - 5x)| - 1) - 4) + 4) + 3| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(3\u03c0(-1|(-3|(-2(-3|x + 2| + 1)^2 + 1(-3|x + 2| + 1) + 2) + 2| + 2) + 3| - 3)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1224", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-2|((2(3cos(3\u03c0(-4x - 3) - 1) + 3) + 2)/(1(3cos(3\u03c0(-4x - 3) - 1) + 3) - 3)) - 3| + 3) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(3|(4(-5(1x^2 - 1x - 3))^2 - 2(-5(1x^2 - 1x - 3)) - 5) - 3| - 1) - 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(1\u03c0(1(-2((3(-1x + 3) + 3)/(2(-1x + 3) - 3)) + 4)^2 - 3) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "242", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(2\u03c0(4(-4((-2((-3x - 1)/(-2x)) + 2)/(-3((-3x - 1)/(-2x)) + 1))) + 4) + 2) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(-1|(2|(-2|((1x + 2)/(-1x - 1)) + 3| - 3) + 2| - 3) + 3|) + 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0(5((2((-3(-3|x| + 3) - 1)/(3(-3|x| + 3))) + 2)/(-1((-3(-3|x| + 3) - 1)/(3(-3|x| + 3))) - 3))^2 + 3((2((-3(-3|x| + 3) - 1)/(3(-3|x| + 3))) + 2)/(-1((-3(-3|x| + 3) - 1)/(3(-3|x| + 3))) - 3)) + 1)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((2(-3((-3(2cos(3\u03c0x + 1)) - 2)/(-1(2cos(3\u03c0x + 1))))^2 + 4((-3(2cos(3\u03c0x + 1)) - 2)/(-1(2cos(3\u03c0x + 1)))) + 4) + 2)/(-2(-3((-3(2cos(3\u03c0x + 1)) - 2)/(-1(2cos(3\u03c0x + 1))))^2 + 4((-3(2cos(3\u03c0x + 1)) - 2)/(-1(2cos(3\u03c0x + 1)))) + 4))) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((-1(-3(-5(3cos(3\u03c0x + 3) - 1) + 3) - 4) + 2)/(1(-3(-5(3cos(3\u03c0x + 3) - 1) + 3) - 4))) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(2|(-2|(-3(-2|x - 3| + 3)^2 + 4(-2|x - 3| + 3) - 3) + 2| + 1)|) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1336", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(3\u03c0(-5(1((3(4x^2 - 2x - 1) + 1)/(-2(4x^2 - 2x - 1) - 1))^2 - 1((3(4x^2 - 2x - 1) + 1)/(-2(4x^2 - 2x - 1) - 1)) - 3) + 3)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(3\u03c0(-3(5(-5((-2x - 3)/(3x + 3))^2 - 5((-2x - 3)/(3x + 3)) - 3) + 5)^2) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "292", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-4(-5((-1(-2cos(1\u03c0x + 2) + 3) - 2)/(3(-2cos(1\u03c0x + 2) + 3) + 1))^2 + 2) + 4)^2 + 3(-4(-5((-1(-2cos(1\u03c0x + 2) + 3) - 2)/(3(-2cos(1\u03c0x + 2) + 3) + 1))^2 + 2) + 4) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(5(5(2(-2e^(2x) + 1) + 3)^2 - 5(2(-2e^(2x) + 1) + 3) - 4)) - 2| + 1 where -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 number of x-intercepts of the function f(x) = 3(-2cos(1\u03c0(2(3|(1x + 1) - 2| - 3)^2 - 3(3|(1x + 1) - 2| - 3) + 3) + 2)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1495", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(2|(3(4(-2sin(1\u03c0x - 2) + 2) - 5) + 2) - 1| - 3) + 2)/(-3(2|(3(4(-2sin(1\u03c0x - 2) + 2) - 5) + 2) - 1| - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-4(5(-2(-1x^2 - 3x + 3) - 1) - 4)^2 - 5(5(-2(-1x^2 - 3x + 3) - 1) - 4) + 3) - 3)/(3(-4(5(-2(-1x^2 - 3x + 3) - 1) - 4)^2 - 5(5(-2(-1x^2 - 3x + 3) - 1) - 4) + 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(3(-3(-2(2sin(1\u03c0x - 1))^2 + 4(2sin(1\u03c0x - 1)) - 1) + 2) + 3)^2 + 1(3(-3(-2(2sin(1\u03c0x - 1))^2 + 4(2sin(1\u03c0x - 1)) - 1) + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(3((-3(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) + 2)/(-1(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) - 3))^2 + 5((-3(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) + 2)/(-1(2((1x + 3)/(-1x))^2 + 2((1x + 3)/(-1x)) - 5) - 3)) - 1) - 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-1(2sin(1\u03c0((1(-2|x + 2| - 1) + 2)/(3(-2|x + 2| - 1) - 2))) + 3)^2 + 2(2sin(1\u03c0((1(-2|x + 2| - 1) + 2)/(3(-2|x + 2| - 1) - 2))) + 3) + 5)^2 + 2(-1(2sin(1\u03c0((1(-2|x + 2| - 1) + 2)/(3(-2|x + 2| - 1) - 2))) + 3)^2 + 2(2sin(1\u03c0((1(-2|x + 2| - 1) + 2)/(3(-2|x + 2| - 1) - 2))) + 3) + 5) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((-1(3(-1cos(1\u03c0(1x^2 - 3x - 1) - 1) + 1) + 1) - 2)/(-3(3(-1cos(1\u03c0(1x^2 - 3x - 1) - 1) + 1) + 1) + 2)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((1(3(1|(-3cos(1\u03c0x) + 2) + 1| - 1) + 1) - 1)/(1(3(1|(-3cos(1\u03c0x) + 2) + 1| - 1) + 1)))^2 + 1((1(3(1|(-3cos(1\u03c0x) + 2) + 1| - 1) + 1) - 1)/(1(3(1|(-3cos(1\u03c0x) + 2) + 1| - 1) + 1))) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(-2(2(5(3|x - 3| - 2) + 2) - 5) + 5) - 1| - 1 where -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 number of x-intercepts of the function f(x) = -3|(-1e^(-2(1|((-1((-2x)/(2x - 1)) - 1)/(-1((-2x)/(2x - 1)) + 2)) - 3| - 1))) + 1| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(1\u03c0(-3|(1(-4(2|x + 1| + 2)^2 - 2(2|x + 1| + 2) - 3)^2 - 4(-4(2|x + 1| + 2)^2 - 2(2|x + 1| + 2) - 3) - 4)| + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "657", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(-2|(-2(-3(-1x - 1)^2 + 2(-1x - 1) - 5) - 4) + 3|)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1419", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(3|(5((1(4x^2 - 1x) - 3)/(-3(4x^2 - 1x) + 1))^2 - 4((1(4x^2 - 1x) - 3)/(-3(4x^2 - 1x) + 1)) - 5) + 2| - 2) - 2 have 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 number of x-intercepts of the function f(x) = 4((-1(4(-1(1|x + 2| - 2))^2 - 2(-1(1|x + 2| - 2)) - 2) + 3)/(-1(4(-1(1|x + 2| - 2))^2 - 2(-1(1|x + 2| - 2)) - 2) - 3)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-4(2sin(3\u03c0(-3(2|x - 2| + 1)^2 + 1(2|x - 2| + 1) - 3) - 2) - 1)^2 + 3(2sin(3\u03c0(-3(2|x - 2| + 1)^2 + 1(2|x - 2| + 1) - 3) - 2) - 1) + 3) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1508", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((1((-3(2cos(1\u03c0(-1x^2 + 5) + 2) + 2) - 3)/(-3(2cos(1\u03c0(-1x^2 + 5) + 2) + 2) + 2)) - 3)/(1((-3(2cos(1\u03c0(-1x^2 + 5) + 2) + 2) - 3)/(-3(2cos(1\u03c0(-1x^2 + 5) + 2) + 2) + 2)) + 2))| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-3|(-3|(-2sin(1\u03c0(-5x - 3) + 2) - 1) + 2| + 3) - 2| + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(2(3(5(2|x + 1| + 1)^2 + 4(2|x + 1| + 1) + 4) - 3)^2 + 4(3(5(2|x + 1| + 1)^2 + 4(2|x + 1| + 1) + 4) - 3)) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "219", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(1((3(-1sin(2\u03c0((-2x - 1)/(3x - 2)) + 2) + 1) - 2)/(1(-1sin(2\u03c0((-2x - 1)/(3x - 2)) + 2) + 1) + 1))^2 - 3((3(-1sin(2\u03c0((-2x - 1)/(3x - 2)) + 2) + 1) - 2)/(1(-1sin(2\u03c0((-2x - 1)/(3x - 2)) + 2) + 1) + 1)) + 4) - 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-5(-3((1(2x^2 - 2x) - 2)/(1(2x^2 - 2x)))^2 - 4((1(2x^2 - 2x) - 2)/(1(2x^2 - 2x)))) - 2)| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(2\u03c0((-2((1(5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 5) + 3)/(-1(5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 5) + 2)) - 1)/(-2((1(5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 5) + 3)/(-1(5(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 5) + 2)) - 2)) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "764", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-3((-1(1cos(1\u03c0(-5x^2 + 4x + 3) - 2) + 1) + 1)/(-1(1cos(1\u03c0(-5x^2 + 4x + 3) - 2) + 1) - 1)) - 1) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "928", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((2(3|(2|(1x - 3) - 2| - 1) - 3| - 1) - 3)/(-3(3|(2|(1x - 3) - 2| - 1) - 3| - 1)))^2 + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(1|((2(-3(1|x - 2| - 2) + 5) - 3)/(2(-3(1|x - 2| - 2) + 5) + 2)) - 3|) - 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(2sin(2\u03c0((1(-1(2x + 3)^2 + 1(2x + 3) + 4))/(-2(-1(2x + 3)^2 + 1(2x + 3) + 4) - 2)) - 1) + 1) - 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(3(2sin(3\u03c0(3|(-3x + 5)| + 3) - 2)) + 1) + 3)/(2(3(2sin(3\u03c0(3|(-3x + 5)| + 3) - 2)) + 1) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-3cos(1\u03c0(4(-1(-2x + 3)^2 + 1(-2x + 3) + 3)) + 1))^2 + 4(-3cos(1\u03c0(4(-1(-2x + 3)^2 + 1(-2x + 3) + 3)) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1593", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(5((3(1(-1x^2 + 5x + 4) + 2) + 2)/(2(1(-1x^2 + 5x + 4) + 2) - 1))^2 + 4((3(1(-1x^2 + 5x + 4) + 2) + 2)/(2(1(-1x^2 + 5x + 4) + 2) - 1)) - 2) - 1)/(2(5((3(1(-1x^2 + 5x + 4) + 2) + 2)/(2(1(-1x^2 + 5x + 4) + 2) - 1))^2 + 4((3(1(-1x^2 + 5x + 4) + 2) + 2)/(2(1(-1x^2 + 5x + 4) + 2) - 1)) - 2) + 2) where -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 number of x-intercepts of the function f(x) = 3sin(3\u03c0(1(4(-4(4x + 5)^2 - 4(4x + 5) - 4) - 3) + 5) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1242", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(-5((-2(-2|(2x^2 + 4x - 5) - 2| + 2) - 3)/(-2(-2|(2x^2 + 4x - 5) - 2| + 2) + 3)) - 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(2|(-1|(4((-3x - 2)/(2x)) + 4)| - 2) - 2| - 1) - 1) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-5(3sin(3\u03c0(-3((-3x)/(2x - 1)) + 2) + 2) + 1)^2 + 2(3sin(3\u03c0(-3((-3x)/(2x - 1)) + 2) + 2) + 1) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(1|((1(1|(1x) + 3| - 1) + 2)/(1(1|(1x) + 3| - 1) + 1)) - 3| - 2) + 2)/(-3(1|((1(1|(1x) + 3| - 1) + 2)/(1(1|(1x) + 3| - 1) + 1)) - 3| - 2) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(2|(1|(-2sin(2\u03c0(3x + 1) - 1) + 1) - 1| - 3) + 1|) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(2(-3((-3(-3sin(3\u03c0x + 3)) - 3)/(1(-3sin(3\u03c0x + 3)))) + 3) + 4) - 2)/(-2(2(-3((-3(-3sin(3\u03c0x + 3)) - 3)/(1(-3sin(3\u03c0x + 3)))) + 3) + 4) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "26", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-2(1e^(-1((-1(-3x + 3) - 1)/(3(-3x + 3)))) - 3)^2 - 3(1e^(-1((-1(-3x + 3) - 1)/(3(-3x + 3)))) - 3) + 3)^2 - 2(-2(1e^(-1((-1(-3x + 3) - 1)/(3(-3x + 3)))) - 3)^2 - 3(1e^(-1((-1(-3x + 3) - 1)/(3(-3x + 3)))) - 3) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(2(-3|(-2|(2x^2 + 3x - 1) - 3|) + 3| - 1)^2 + 2(-3|(-2|(2x^2 + 3x - 1) - 3|) + 3| - 1) - 2)^2 - 3(2(-3|(-2|(2x^2 + 3x - 1) - 3|) + 3| - 1)^2 + 2(-3|(-2|(2x^2 + 3x - 1) - 3|) + 3| - 1) - 2) - 5 have 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 number of x-intercepts of the function f(x) = 2(-3sin(3\u03c0((1(-3(4x^2 + 5x) - 1) + 1)/(-3(-3(4x^2 + 5x) - 1) + 4)) + 3) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-2cos(1\u03c0(2((3(-5x - 2) + 3)/(-1(-5x - 2)))^2 + 3((3(-5x - 2) + 3)/(-1(-5x - 2))) + 1) - 2) - 1) - 3)/(-1(-2cos(1\u03c0(2((3(-5x - 2) + 3)/(-1(-5x - 2)))^2 + 3((3(-5x - 2) + 3)/(-1(-5x - 2))) + 1) - 2) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(1((-2(1cos(2\u03c0((1x + 2)/(-3x - 1))) + 2) - 1)/(3(1cos(2\u03c0((1x + 2)/(-3x - 1))) + 2) - 2))^2 - 1)^2 + 5(1((-2(1cos(2\u03c0((1x + 2)/(-3x - 1))) + 2) - 1)/(3(1cos(2\u03c0((1x + 2)/(-3x - 1))) + 2) - 2))^2 - 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1|(2|(-2cos(3\u03c0(-5x^2 + 5x + 5)) + 3) + 2| - 3) - 2| - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1453", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4((2(3(5(2sin(3\u03c0x - 2) - 1)^2 - 4(2sin(3\u03c0x - 2) - 1)) - 2))/(1(3(5(2sin(3\u03c0x - 2) - 1)^2 - 4(2sin(3\u03c0x - 2) - 1)) - 2) + 1))^2 + 1((2(3(5(2sin(3\u03c0x - 2) - 1)^2 - 4(2sin(3\u03c0x - 2) - 1)) - 2))/(1(3(5(2sin(3\u03c0x - 2) - 1)^2 - 4(2sin(3\u03c0x - 2) - 1)) - 2) + 1)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "195", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|((-2((2(-2|(-1x^2 + 5x + 1)| + 1) - 1)/(2(-2|(-1x^2 + 5x + 1)| + 1) - 3)) - 1)/(2((2(-2|(-1x^2 + 5x + 1)| + 1) - 1)/(2(-2|(-1x^2 + 5x + 1)| + 1) - 3)) - 1))| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(3cos(3\u03c0(1(-2|(-4x + 3)| - 1) - 5) - 1) - 2) + 2)/(3(3cos(3\u03c0(1(-2|(-4x + 3)| - 1) - 5) - 1) - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "237", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((1(-3(2cos(3\u03c0(-1|x + 1| - 1) + 1) + 2) + 1) + 2)/(-2(-3(2cos(3\u03c0(-1|x + 1| - 1) + 1) + 2) + 1) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1(-3sin(3\u03c0(4(3|x + 2| - 2) + 2) + 1) - 1)^2 + 4(-3sin(3\u03c0(4(3|x + 2| - 2) + 2) + 1) - 1) - 5)^2 - 5(1(-3sin(3\u03c0(4(3|x + 2| - 2) + 2) + 1) - 1)^2 + 4(-3sin(3\u03c0(4(3|x + 2| - 2) + 2) + 1) - 1) - 5) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "369", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(1\u03c0(-3(-3(-2|((-3x - 3)/(-3x + 1)) + 1| - 2)^2 - 1(-2|((-3x - 3)/(-3x + 1)) + 1| - 2) - 4) - 1) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "332", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3|(1(-1|(-3x^2 + 3x - 1) - 1| + 1)^2 + 5(-1|(-3x^2 + 3x - 1) - 1| + 1) - 1) - 2|)^2 - 2(3|(1(-1|(-3x^2 + 3x - 1) - 1| + 1)^2 + 5(-1|(-3x^2 + 3x - 1) - 1| + 1) - 1) - 2|) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-4(4(-1((-1x + 3)/(-3x + 4)) - 4)^2 + 4(-1((-1x + 3)/(-3x + 4)) - 4) + 2)^2 + 5(4(-1((-1x + 3)/(-3x + 4)) - 4)^2 + 4(-1((-1x + 3)/(-3x + 4)) - 4) + 2) + 2)^2 - 4(-4(4(-1((-1x + 3)/(-3x + 4)) - 4)^2 + 4(-1((-1x + 3)/(-3x + 4)) - 4) + 2)^2 + 5(4(-1((-1x + 3)/(-3x + 4)) - 4)^2 + 4(-1((-1x + 3)/(-3x + 4)) - 4) + 2) + 2) - 4 have 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 number of x-intercepts of the function f(x) = 2sin(3\u03c0(1(2|(-2|(1|x - 3| + 3) - 1| - 2) - 1| - 1) + 2)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2((2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 2)/(2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 1))^2 + 4((2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 2)/(2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 1)) - 2)^2 + 2(2((2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 2)/(2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 1))^2 + 4((2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 2)/(2((-2(-3x - 4))/(-2(-3x - 4) - 3)) - 1)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(-3((-3(-3cos(1\u03c0(-1x^2 - 3x - 2) + 3) - 1) - 3)/(3(-3cos(1\u03c0(-1x^2 - 3x - 2) + 3) - 1) + 2))^2 + 1((-3(-3cos(1\u03c0(-1x^2 - 3x - 2) + 3) - 1) - 3)/(3(-3cos(1\u03c0(-1x^2 - 3x - 2) + 3) - 1) + 2)) + 5) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "325", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-1(2(3cos(3\u03c0(-1|x - 1| + 1) + 3))^2 - 4)^2 + 1(2(3cos(3\u03c0(-1|x - 1| + 1) + 3))^2 - 4) + 1)| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-3(1(4(2cos(3\u03c0x - 2) + 2) - 4)^2 - 5(4(2cos(3\u03c0x - 2) + 2) - 4) - 2)^2 - 1(1(4(2cos(3\u03c0x - 2) + 2) - 4)^2 - 5(4(2cos(3\u03c0x - 2) + 2) - 4) - 2) + 5) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-1|(2|(2|(5x^2 - 5x - 2) - 1|) + 1| - 2) + 1| + 2)^2 + 3(-1|(2|(2|(5x^2 - 5x - 2) - 1|) + 1| - 2) + 1| + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(1(2sin(3\u03c0(-2|(1|x + 3| + 2) - 3| + 2) - 2) + 1)^2 + 3(2sin(3\u03c0(-2|(1|x + 3| + 2) - 3| + 2) - 2) + 1)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(3(3|((-2(-2|x + 2| - 3) + 1)/(1(-2|x + 2| - 3) + 3)) + 2| - 2)^2 - 4(3|((-2(-2|x + 2| - 3) + 1)/(1(-2|x + 2| - 3) + 3)) + 2| - 2) + 1) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "276", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(3sin(1\u03c0(2|((1(2|x - 3| - 1))/(-1(2|x - 3| - 1) - 1)) + 1| - 1) - 1) + 2) - 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2((2((-2(1|(-4x^2 + 2x + 5) + 2| - 2) - 2)/(3(1|(-4x^2 + 2x + 5) + 2| - 2) + 2)) - 3)/(-3((-2(1|(-4x^2 + 2x + 5) + 2| - 2) - 2)/(3(1|(-4x^2 + 2x + 5) + 2| - 2) + 2)))) - 3)/(-2((2((-2(1|(-4x^2 + 2x + 5) + 2| - 2) - 2)/(3(1|(-4x^2 + 2x + 5) + 2| - 2) + 2)) - 3)/(-3((-2(1|(-4x^2 + 2x + 5) + 2| - 2) - 2)/(3(1|(-4x^2 + 2x + 5) + 2| - 2) + 2)))) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(2sin(3\u03c0((-1(-2((-1x - 2)/(3x - 1))^2 + 2((-1x - 2)/(3x - 1)) + 5) + 1)/(-1(-2((-1x - 2)/(3x - 1))^2 + 2((-1x - 2)/(3x - 1)) + 5) - 2)) + 3) + 3) - 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(3e^(1(-1((1(3x^2 - 1x) - 2)/(-2(3x^2 - 1x) - 2))^2 - 5((1(3x^2 - 1x) - 2)/(-2(3x^2 - 1x) - 2)) + 3)) - 2)^2 + 2(3e^(1(-1((1(3x^2 - 1x) - 2)/(-2(3x^2 - 1x) - 2))^2 - 5((1(3x^2 - 1x) - 2)/(-2(3x^2 - 1x) - 2)) + 3)) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(1(-4(-1|(-3cos(3\u03c0x - 2) - 3) + 3| + 1)^2 + 5(-1|(-3cos(3\u03c0x - 2) - 3) + 3| + 1) + 3) - 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "167", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(5(1(-3(1|x + 3| - 3))^2 - 3(-3(1|x + 3| - 3))) + 3)^2 + 4(5(1(-3(1|x + 3| - 3))^2 - 3(-3(1|x + 3| - 3))) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0((-2(-1|(-1(-3x^2 + 1x + 4)^2 - 5(-3x^2 + 1x + 4) + 5) - 2| + 3) + 2)/(1(-1|(-1(-3x^2 + 1x + 4)^2 - 5(-3x^2 + 1x + 4) + 5) - 2| + 3))) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(2sin(3\u03c0(3(-3|((1x)/(3x + 3))| + 2) - 3) + 2) + 2) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1sin(2\u03c0((3(-2|(-1((-3x)/(2x - 1))^2 + 5) - 3| + 1) + 3)/(3(-2|(-1((-3x)/(2x - 1))^2 + 5) - 3| + 1) - 2))) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-5(3sin(2\u03c0(-5(2|x - 1| + 3)^2 + 2(2|x - 1| + 3) + 4) - 3) - 1) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1430", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-3(3|(-4((-1x + 1)/(3x - 1))^2 + 2((-1x + 1)/(3x - 1)) + 5)| - 2))^2 - 5(-3(3|(-4((-1x + 1)/(3x - 1))^2 + 2((-1x + 1)/(3x - 1)) + 5)| - 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-3((-3((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) + 3)/(2((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) - 1)) + 2)/(3((-3((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) + 3)/(2((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) - 1)) - 1))^2 + 4((-3((-3((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) + 3)/(2((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) - 1)) + 2)/(3((-3((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) + 3)/(2((-2(-3|x - 3| - 3) - 2)/(-1(-3|x - 3| - 3) + 2)) - 1)) - 1)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0(-3|(-3(-2|(-2x^2 - 4x - 3) + 1| - 2) + 1) - 1| - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1566", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-3|(-1|(-2|(-1sin(3\u03c0x - 3)) + 1|) + 1| - 1) + 3| + 2) + 2)/(1(-3|(-1|(-2|(-1sin(3\u03c0x - 3)) + 1|) + 1| - 1) + 3| + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5((1(-2|((-2(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1) - 3)) - 2| + 2) - 3)/(-3(-2|((-2(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1) - 3)) - 2| + 2) + 1))^2 - 2((1(-2|((-2(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1) - 3)) - 2| + 2) - 3)/(-3(-2|((-2(-2|x - 2| - 1) + 1)/(-2(-2|x - 2| - 1) - 3)) - 2| + 2) + 1)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-1(-1(-2sin(2\u03c0((2x + 1)/(-1x + 2)) + 1) - 1)^2 + 5(-2sin(2\u03c0((2x + 1)/(-1x + 2)) + 1) - 1) - 5)^2 - 1(-1(-2sin(2\u03c0((2x + 1)/(-1x + 2)) + 1) - 1)^2 + 5(-2sin(2\u03c0((2x + 1)/(-1x + 2)) + 1) - 1) - 5) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-2(-1sin(1\u03c0(1((-1x - 1)/(2x))^2 + 4((-1x - 1)/(2x)) + 5) + 3) + 2) + 1)^2 + 3(-2(-1sin(1\u03c0(1((-1x - 1)/(2x))^2 + 4((-1x - 1)/(2x)) + 5) + 3) + 2) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(1\u03c0(3(-5(-1(-4x - 2) - 2))^2 + 2(-5(-1(-4x - 2) - 2)) - 3) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1298", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-2|(2|((-3(-2x^2 - 2x - 2) + 2)/(-2(-2x^2 - 2x - 2) - 3)) - 2| - 2) - 2|)^2 - 4(-2|(2|((-3(-2x^2 - 2x - 2) + 2)/(-2(-2x^2 - 2x - 2) - 3)) - 2| - 2) - 2|) + 5 have 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 number of x-intercepts of the function f(x) = -4((2(-3sin(2\u03c0(1(-4x - 2)^2 + 2(-4x - 2) + 5))) + 1)/(3(-3sin(2\u03c0(1(-4x - 2)^2 + 2(-4x - 2) + 5))))) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "141", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(2(2(2(-3cos(2\u03c0x - 1) + 1) - 2)^2 - 4(2(-3cos(2\u03c0x - 1) + 1) - 2) - 1) - 5) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3cos(3\u03c0(-5(2(-5x^2 + 1) - 2)^2 - 2(2(-5x^2 + 1) - 2) - 5)) - 1)^2 + 5(3cos(3\u03c0(-5(2(-5x^2 + 1) - 2)^2 - 2(2(-5x^2 + 1) - 2) - 5)) - 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "258", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-2((-3(1(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1)) - 2)/(2(1(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1)) - 1)) + 1)/(1((-3(1(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1)) - 2)/(2(1(-1|x - 3| + 1)^2 + 3(-1|x - 3| + 1)) - 1)) - 2)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0(-3|(2(-5(-2|x| + 3)^2 + 1(-2|x| + 3) - 4) + 5) + 2| + 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1578", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0(1|(-1|((-2(-3|x + 1| - 1) - 2)/(1(-3|x + 1| - 1) + 2)) + 3| - 2) + 3| + 1) + 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(1(2(-3((-2x - 2)/(-3x + 2))^2 - 1((-2x - 2)/(-3x + 2)) - 1)^2 - 2(-3((-2x - 2)/(-3x + 2))^2 - 1((-2x - 2)/(-3x + 2)) - 1) - 4)^2 + 2(2(-3((-2x - 2)/(-3x + 2))^2 - 1((-2x - 2)/(-3x + 2)) - 1)^2 - 2(-3((-2x - 2)/(-3x + 2))^2 - 1((-2x - 2)/(-3x + 2)) - 1) - 4) + 2) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "621", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(-4(-1((-3(-3x + 1) + 1)/(1(-3x + 1) - 3))^2 - 4((-3(-3x + 1) + 1)/(1(-3x + 1) - 3)) + 2) + 1) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "257", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(-1(3(-2(-2x^2 - 3x - 4))^2 - 5(-2(-2x^2 - 3x - 4)) - 5)^2 - 5(3(-2(-2x^2 - 3x - 4))^2 - 5(-2(-2x^2 - 3x - 4)) - 5) - 4) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "151", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2(-2(-1(-3cos(1\u03c0x + 2) + 3) + 2) - 3)^2 + 5) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-1|(1|((3(-5x^2 - 2x - 1) + 1)/(-3(-5x^2 - 2x - 1) - 3)) + 3|) - 2| + 3) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((3(-3cos(2\u03c0((1((-2x + 2)/(-2x)) - 3)/(-1((-2x + 2)/(-2x)) - 2)) - 1) - 2) + 2)/(2(-3cos(2\u03c0((1((-2x + 2)/(-2x)) - 3)/(-1((-2x + 2)/(-2x)) - 2)) - 1) - 2))) + 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-1|(1|(-1|(3x - 1) - 2| + 1) + 3| - 3)| + 2)^2 + 2(-1|(1|(-1|(3x - 1) - 2| + 1) + 3| - 3)| + 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((-3(2(3sin(1\u03c0(-3|x + 1| + 2) - 3) - 2)^2 + 5(3sin(1\u03c0(-3|x + 1| + 2) - 3) - 2) + 2) - 3)/(-2(2(3sin(1\u03c0(-3|x + 1| + 2) - 3) - 2)^2 + 5(3sin(1\u03c0(-3|x + 1| + 2) - 3) - 2) + 2) - 1))^2 + 4((-3(2(3sin(1\u03c0(-3|x + 1| + 2) - 3) - 2)^2 + 5(3sin(1\u03c0(-3|x + 1| + 2) - 3) - 2) + 2) - 3)/(-2(2(3sin(1\u03c0(-3|x + 1| + 2) - 3) - 2)^2 + 5(3sin(1\u03c0(-3|x + 1| + 2) - 3) - 2) + 2) - 1)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "246", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2|((3(-3(2x - 2)^2 - 5(2x - 2) - 1) + 2)/(-1(-3(2x - 2)^2 - 5(2x - 2) - 1) - 3)) - 3| + 1) + 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0(1|((-2(3|(2x + 5) - 1| - 2) + 1)/(-3(3|(2x + 5) - 1| - 2) - 1)) - 1| - 1) - 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(1(4(2cos(3\u03c0((1x - 2)/(3x)) + 2) - 2)^2 - 1(2cos(3\u03c0((1x - 2)/(3x)) + 2) - 2) - 1) - 4)^2 + 1(1(4(2cos(3\u03c0((1x - 2)/(3x)) + 2) - 2)^2 - 1(2cos(3\u03c0((1x - 2)/(3x)) + 2) - 2) - 1) - 4) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(-1|(-2|((1(-2|x - 1| + 2) - 1)/(3(-2|x - 1| + 2) - 2)) + 1|) + 3| + 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-5(3(-3sin(1\u03c0((-2x + 2)/(-1x - 2)) + 1) + 3) - 3) + 4) - 1| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(2\u03c0((-3(3|(2(4x + 1)^2 + 3(4x + 1) - 3)| - 1) + 2)/(2(3|(2(4x + 1)^2 + 3(4x + 1) - 3)| - 1) + 3))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(2sin(3\u03c0(-1|(-1(-2x - 4)^2 + 3(-2x - 4))| + 2) + 2) + 3) - 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1219", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((-1((-2(2(2cos(3\u03c0x - 1) + 1)^2 - 1(2cos(3\u03c0x - 1) + 1) - 4) - 3)/(3(2(2cos(3\u03c0x - 1) + 1)^2 - 1(2cos(3\u03c0x - 1) + 1) - 4) + 3)))/(1((-2(2(2cos(3\u03c0x - 1) + 1)^2 - 1(2cos(3\u03c0x - 1) + 1) - 4) - 3)/(3(2(2cos(3\u03c0x - 1) + 1)^2 - 1(2cos(3\u03c0x - 1) + 1) - 4) + 3)) - 2))| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "143", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(3sin(3\u03c0(-5(-3(3|x| - 3)^2 - 1(3|x| - 3) - 1)^2 - 2(-3(3|x| - 3)^2 - 1(3|x| - 3) - 1) + 5) - 2) - 3) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "356", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|((-3(3(1((-3x + 1)/(2x + 2))^2 - 5((-3x + 1)/(2x + 2)) - 5)^2 + 4(1((-3x + 1)/(2x + 2))^2 - 5((-3x + 1)/(2x + 2)) - 5) - 3) + 2)/(1(3(1((-3x + 1)/(2x + 2))^2 - 5((-3x + 1)/(2x + 2)) - 5)^2 + 4(1((-3x + 1)/(2x + 2))^2 - 5((-3x + 1)/(2x + 2)) - 5) - 3) + 3)) - 3| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-2|(4(-2|(-3|x - 3| - 2) + 3| + 3)^2 - 3(-2|(-3|x - 3| - 2) + 3| + 3) - 3)| + 3) - 1)/(-3(-2|(4(-2|(-3|x - 3| - 2) + 3| + 3)^2 - 3(-2|(-3|x - 3| - 2) + 3| + 3) - 3)| + 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(2(-5(1(-2cos(3\u03c0x + 1) - 2)^2 - 3) - 2)) + 2| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-1(-3(-4(1|x| - 3) - 4)^2 - 4(-4(1|x| - 3) - 4) - 3) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(4(1(3(-1x^2 - 5x - 2)^2 - 4(-1x^2 - 5x - 2) + 1) - 1) + 1)^2 - 5(4(1(3(-1x^2 - 5x - 2)^2 - 4(-1x^2 - 5x - 2) + 1) - 1) + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(3|((-1(3|(-2|x - 2| - 1) + 3| - 3) + 3)/(3(3|(-2|x - 2| - 1) + 3| - 3) - 2)) + 1|))/(-3(3|((-1(3|(-2|x - 2| - 1) + 3| - 3) + 3)/(3(3|(-2|x - 2| - 1) + 3| - 3) - 2)) + 1|) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-4(-1|((-2(-3x - 3))/(3(-3x - 3) - 2)) - 2| + 2)^2 + 5(-1|((-2(-3x - 3))/(3(-3x - 3) - 2)) - 2| + 2) + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-5((1((-3(3x) + 3)/(-2(3x))) + 3)/(-2((-3(3x) + 3)/(-2(3x))) - 2))^2 + 4)^2 - 2(-5((1((-3(3x) + 3)/(-2(3x))) + 3)/(-2((-3(3x) + 3)/(-2(3x))) - 2))^2 + 4) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(-2sin(1\u03c0(3((1(5x + 2) - 1)/(-1(5x + 2) + 3)) + 4) - 1) - 1) - 2)/(1(-2sin(1\u03c0(3((1(5x + 2) - 1)/(-1(5x + 2) + 3)) + 4) - 1) - 1) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-4(-4(-3(1x^2 + 1x - 5)^2 - 1(1x^2 + 1x - 5) + 5) + 1)^2 - 2(-4(-3(1x^2 + 1x - 5)^2 - 1(1x^2 + 1x - 5) + 5) + 1) + 4)^2 - 1(-4(-4(-3(1x^2 + 1x - 5)^2 - 1(1x^2 + 1x - 5) + 5) + 1)^2 - 2(-4(-3(1x^2 + 1x - 5)^2 - 1(1x^2 + 1x - 5) + 5) + 1) + 4) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(-3(2cos(1\u03c0(-1(-1x - 3) + 3) + 1))^2 + 5(2cos(1\u03c0(-1(-1x - 3) + 3) + 1)) - 1) + 3| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|((3(1((1(4x^2 + 4x - 3) - 1)/(1(4x^2 + 4x - 3))) - 5) - 1)/(1(1((1(4x^2 + 4x - 3) - 1)/(1(4x^2 + 4x - 3))) - 5) + 2))| + 1 where -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 number of x-intercepts of the function f(x) = -3|(2((1(3|(1x - 5)| - 3) + 2)/(3(3|(1x - 5)| - 3) - 2)) - 1) - 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2\u03c0(1|(1|((-3(3|x| + 3) + 3)/(1(3|x| + 3) - 3)) + 1| - 3)| - 3) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1|((2(-4(2sin(1\u03c0x + 2) - 1) - 3) + 1)/(-1(-4(2sin(1\u03c0x + 2) - 1) - 3))) - 3| + 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((-1((1(-3sin(2\u03c0(-1x - 3) - 2) - 1) + 3)/(-1(-3sin(2\u03c0(-1x - 3) - 2) - 1) + 2)) - 3)/(3((1(-3sin(2\u03c0(-1x - 3) - 2) - 1) + 3)/(-1(-3sin(2\u03c0(-1x - 3) - 2) - 1) + 2)) - 2)) + 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(1\u03c0(-4(1(-1(-2|x + 3| - 3) - 4) - 4)^2 + 2(1(-1(-2|x + 3| - 3) - 4) - 4) + 2) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1252", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-2|(4(-1(-1|x - 2| + 1)^2 + 2(-1|x - 2| + 1) + 2) - 2) + 2| + 1) - 3 where -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 number of x-intercepts of the function f(x) = -5(-3|((-3(-5((2x - 2)/(1x + 2))^2 + 1((2x - 2)/(1x + 2)) + 5) + 3)/(-2(-5((2x - 2)/(1x + 2))^2 + 1((2x - 2)/(1x + 2)) + 5) - 2)) + 2| + 2) - 2 where -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 number of x-intercepts of the function f(x) = 3(-1sin(3\u03c0((1((-2(1|x - 1| + 3) + 1)/(3(1|x - 1| + 3) + 1)) - 3)/(3((-2(1|x - 1| + 3) + 1)/(3(1|x - 1| + 3) + 1)) + 1)) - 2) + 2)^2 - 3(-1sin(3\u03c0((1((-2(1|x - 1| + 3) + 1)/(3(1|x - 1| + 3) + 1)) - 3)/(3((-2(1|x - 1| + 3) + 1)/(3(1|x - 1| + 3) + 1)) + 1)) - 2) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-5(1|(-1|(-1x^2 + 3x + 5) + 2| + 2) - 1| - 3) + 1)^2 - 3(-5(1|(-1|(-1x^2 + 3x + 5) + 2| + 2) - 1| - 3) + 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(2|((-2(-3cos(1\u03c0(-2x) - 1) - 2) + 2)/(2(-3cos(1\u03c0(-2x) - 1) - 2) + 1)) + 2| - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|((-1(-1e^(1(5(3|x + 1| - 3) + 2)) + 3) - 2)/(1(-1e^(1(5(3|x + 1| - 3) + 2)) + 3) - 3)) - 2| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(2|(4(2(5x^2 - 1x - 4) + 3) + 4) + 3| + 1)^2 + 4(2|(4(2(5x^2 - 1x - 4) + 3) + 4) + 3| + 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-1sin(1\u03c0(5(3|(-5x + 2) + 1| - 1)) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1499", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3\u03c0(1(4(1(4x^2 + 2x + 2)^2 + 3(4x^2 + 2x + 2) + 3) - 2) - 3) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1059", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0(-5((1(1(1|x| + 1) - 1) + 3)/(2(1(1|x| + 1) - 1) + 2))^2 + 3((1(1(1|x| + 1) - 1) + 3)/(2(1(1|x| + 1) - 1) + 2)) - 5) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(2|(-2(-2(2|x + 1| - 3) + 2) + 4) - 1| - 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "640", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(1|(1|(-3e^(-2((-2x + 1)/(-1x - 3)))) - 1| - 3) - 2| - 2) + 1| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|((-2(2sin(1\u03c0((2(-3x^2 + 3x + 3))/(2(-3x^2 + 3x + 3) - 1)) - 3) + 2))/(-3(2sin(1\u03c0((2(-3x^2 + 3x + 3))/(2(-3x^2 + 3x + 3) - 1)) - 3) + 2) + 4)) + 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((-3((-1(-2(-2sin(1\u03c0x + 3) + 2)^2 + 5(-2sin(1\u03c0x + 3) + 2)) + 2)/(3(-2(-2sin(1\u03c0x + 3) + 2)^2 + 5(-2sin(1\u03c0x + 3) + 2)) + 3)) - 1)/(1((-1(-2(-2sin(1\u03c0x + 3) + 2)^2 + 5(-2sin(1\u03c0x + 3) + 2)) + 2)/(3(-2(-2sin(1\u03c0x + 3) + 2)^2 + 5(-2sin(1\u03c0x + 3) + 2)) + 3)) + 3)) - 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(2|(-1cos(3\u03c0(5(1x)^2 + 3(1x) - 2)) + 1) + 2|)^2 + 5(2|(-1cos(3\u03c0(5(1x)^2 + 3(1x) - 2)) + 1) + 2|) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1622", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(-5(3|(1(-5x + 4)^2 - 4(-5x + 4) + 5) - 2|) + 5) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1230", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-1|(-1cos(3\u03c0(-2(2x^2 + 1) - 2) - 2) + 3) - 2|)^2 + 3(-1|(-1cos(3\u03c0(-2(2x^2 + 1) - 2) - 2) + 3) - 2|) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "978", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-3(3(1sin(2\u03c0((3x + 3)/(-2x)) - 3) - 1)^2 - 4(1sin(2\u03c0((3x + 3)/(-2x)) - 3) - 1) + 1) + 4) + 3| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(5(3(1(-4x + 2)^2 + 3(-4x + 2) - 5) + 1)^2 + 1(3(1(-4x + 2)^2 + 3(-4x + 2) - 5) + 1) - 3)^2 - 4(5(3(1(-4x + 2)^2 + 3(-4x + 2) - 5) + 1)^2 + 1(3(1(-4x + 2)^2 + 3(-4x + 2) - 5) + 1) - 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1((2(-1sin(1\u03c0(3(-4x^2 + 4x) - 3) + 1) - 3) + 2)/(1(-1sin(1\u03c0(3(-4x^2 + 4x) - 3) + 1) - 3))) + 1)/(-1((2(-1sin(1\u03c0(3(-4x^2 + 4x) - 3) + 1) - 3) + 2)/(1(-1sin(1\u03c0(3(-4x^2 + 4x) - 3) + 1) - 3))) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "946", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0(2|(1(1|((3x + 2)/(2x - 1)) - 3| - 1) - 5) - 2| - 2) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(2sin(1\u03c0((-3((2(-5x - 1) + 2)/(1(-5x - 1) - 2)) - 3)/(-1((2(-5x - 1) + 2)/(1(-5x - 1) - 2)) - 2))) + 2)^2 - 1(2sin(1\u03c0((-3((2(-5x - 1) + 2)/(1(-5x - 1) - 2)) - 3)/(-1((2(-5x - 1) + 2)/(1(-5x - 1) - 2)) - 2))) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-3sin(3\u03c0(3(5(2|x + 2|)^2 + 3(2|x + 2|))^2 - 1(5(2|x + 2|)^2 + 3(2|x + 2|)) + 2) - 2) + 1) + 1)/(-3(-3sin(3\u03c0(3(5(2|x + 2|)^2 + 3(2|x + 2|))^2 - 1(5(2|x + 2|)^2 + 3(2|x + 2|)) + 2) - 2) + 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3(1cos(3\u03c0(-5(-5x + 3) - 4) - 1) + 1) - 5) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1500", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-4(3((-2(2cos(1\u03c0x - 3) - 2) - 2)/(2(2cos(1\u03c0x - 3) - 2) - 1)) - 3) + 2) - 3)/(1(-4(3((-2(2cos(1\u03c0x - 3) - 2) - 2)/(2(2cos(1\u03c0x - 3) - 2) - 1)) - 3) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(4(-2(-4(4x^2 + 3x - 3)^2 - 1(4x^2 + 3x - 3) + 5) - 2) + 5)^2 + 5(4(-2(-4(4x^2 + 3x - 3)^2 - 1(4x^2 + 3x - 3) + 5) - 2) + 5) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(5(-2(5(-2|x - 3| - 3) + 1) - 5) + 4) - 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2000", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(2|((2(-2(2|x| - 2)^2 - 4(2|x| - 2) - 4))/(-2(-2(2|x| - 2)^2 - 4(2|x| - 2) - 4) + 3)) + 3| + 1) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(2sin(1\u03c0(3(-3|(-1x^2 - 3x + 3) - 3|)) - 2) + 1) + 2| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1133", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-2(2(-2|(-1x^2 + 3x + 1) - 1| + 3)^2 - 3(-2|(-1x^2 + 3x + 1) - 1| + 3) - 5) - 4)^2 - 1 have 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 number of x-intercepts of the function f(x) = (3((3(-2|(-1|((2x - 1)/(-1x + 2))| + 2) - 1| - 1) + 3)/(-1(-2|(-1|((2x - 1)/(-1x + 2))| + 2) - 1| - 1) - 3)) - 2)/(1((3(-2|(-1|((2x - 1)/(-1x + 2))| + 2) - 1| - 1) + 3)/(-1(-2|(-1|((2x - 1)/(-1x + 2))| + 2) - 1| - 1) - 3)) - 2) where -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 number of x-intercepts of the function f(x) = 4(-3cos(3\u03c0(-1(-4(1x^2 + 5x + 4)^2 - 5(1x^2 + 5x + 4) - 3)^2 - 4) - 3) - 3)^2 - 5(-3cos(3\u03c0(-1(-4(1x^2 + 5x + 4)^2 - 5(1x^2 + 5x + 4) - 3)^2 - 4) - 3) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "206", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(2(-1(-3|(4x + 3) - 3| + 1)^2 - 3(-3|(4x + 3) - 3| + 1) - 4)^2 + 4(-1(-3|(4x + 3) - 3| + 1)^2 - 3(-3|(4x + 3) - 3| + 1) - 4) - 1) + 2)/(3(2(-1(-3|(4x + 3) - 3| + 1)^2 - 3(-3|(4x + 3) - 3| + 1) - 4)^2 + 4(-1(-3|(4x + 3) - 3| + 1)^2 - 3(-3|(4x + 3) - 3| + 1) - 4) - 1) + 2) have 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 number of x-intercepts of the function f(x) = (-1(-5(-1(-1(-4x + 3) + 2)^2 - 1(-1(-4x + 3) + 2) + 1)^2 - 5(-1(-1(-4x + 3) + 2)^2 - 1(-1(-4x + 3) + 2) + 1) - 1) - 2)/(2(-5(-1(-1(-4x + 3) + 2)^2 - 1(-1(-4x + 3) + 2) + 1)^2 - 5(-1(-1(-4x + 3) + 2)^2 - 1(-1(-4x + 3) + 2) + 1) - 1) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(3\u03c0((-3(3|(-2(-1x^2 - 3x + 4) + 4) + 3| - 2) - 1)/(-1(3|(-2(-1x^2 - 3x + 4) + 4) + 3| - 2) + 3)) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3e^(-1((-1(-2|(5((-2x + 2)/(3x + 3))^2 + 3((-2x + 2)/(3x + 3)) - 2) - 2| + 1) + 1)/(3(-2|(5((-2x + 2)/(3x + 3))^2 + 3((-2x + 2)/(3x + 3)) - 2) - 2| + 1) + 2))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(-1(-2(5((1x)/(2x - 1)) - 3) + 1)^2 + 5(-2(5((1x)/(2x - 1)) - 3) + 1) + 5)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "152", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-3(2sin(3\u03c0(-5((3x + 1)/(2x - 1)) + 5) - 3) + 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "159", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(2cos(2\u03c0(1|(2(-2|x - 1|)^2 - 5(-2|x - 1|) - 5) + 3| - 3) - 2))^2 - 4(2cos(2\u03c0(1|(2(-2|x - 1|)^2 - 5(-2|x - 1|) - 5) + 3| - 3) - 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1763", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1cos(1\u03c0(5(-2|(-3x^2 - 1x + 3) + 1| - 1)^2 - 5(-2|(-3x^2 - 1x + 3) + 1| - 1)) + 3) + 1) + 1)/(2(-1cos(1\u03c0(5(-2|(-3x^2 - 1x + 3) + 1| - 1)^2 - 5(-2|(-3x^2 - 1x + 3) + 1| - 1)) + 3) + 1) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "486", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-2cos(3\u03c0(2((3(-1x^2 + 5x - 1) + 2)/(-2(-1x^2 + 5x - 1) + 1)) + 2) - 2)) + 3)/(-2(-2cos(3\u03c0(2((3(-1x^2 + 5x - 1) + 2)/(-2(-1x^2 + 5x - 1) + 1)) + 2) - 2)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-1(5(1(-1x^2 - 5x - 3) - 2)) - 1)^2 - 5(-1(5(1(-1x^2 - 5x - 3) - 2)) - 1) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1((-2(-2((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))^2 - 4((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))) + 1)/(2(-2((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))^2 - 4((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))) + 1)) - 2)/(3((-2(-2((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))^2 - 4((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))) + 1)/(2(-2((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))^2 - 4((3(-1x^2 + 3x + 4) + 1)/(1(-1x^2 + 3x + 4) - 3))) + 1)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-2cos(2\u03c0(-2(5(-5x^2 - 1x + 5)^2 - 5(-5x^2 - 1x + 5) - 1)^2 - 2(5(-5x^2 - 1x + 5)^2 - 5(-5x^2 - 1x + 5) - 1) - 2) - 2) + 3) - 1)/(1(-2cos(2\u03c0(-2(5(-5x^2 - 1x + 5)^2 - 5(-5x^2 - 1x + 5) - 1)^2 - 2(5(-5x^2 - 1x + 5)^2 - 5(-5x^2 - 1x + 5) - 1) - 2) - 2) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "142", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1(3|(-4((-2x - 3)/(-2x + 3))^2 - 4((-2x - 3)/(-2x + 3)) + 4) - 1|) - 4)^2 + 3(1(3|(-4((-2x - 3)/(-2x + 3))^2 - 4((-2x - 3)/(-2x + 3)) + 4) - 1|) - 4) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(2sin(2\u03c0(1|(-2|((-1x + 3)/(-2x + 1)) - 3| + 1) + 3| - 2) - 1)) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3((-3(4(-2(-3|x - 1| + 2)^2 + 1(-3|x - 1| + 2))^2 - 3) - 3)/(-1(4(-2(-3|x - 1| + 2)^2 + 1(-3|x - 1| + 2))^2 - 3) + 2)) + 3)/(-3((-3(4(-2(-3|x - 1| + 2)^2 + 1(-3|x - 1| + 2))^2 - 3) - 3)/(-1(4(-2(-3|x - 1| + 2)^2 + 1(-3|x - 1| + 2))^2 - 3) + 2)) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1sin(3\u03c0((1(3|(-1x - 3)|) + 1)/(-3(3|(-1x - 3)|))) - 3) + 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-3e^(2(1|(-4(-1|x| + 2)^2 - 3(-1|x| + 2) + 4)| - 1)) + 3) + 3)/(-2(-3e^(2(1|(-4(-1|x| + 2)^2 - 3(-1|x| + 2) + 4)| - 1)) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(-2(-3|(1((-2x - 3)/(-3x + 4))^2 + 3((-2x - 3)/(-3x + 4)) - 2) + 3| + 2)^2 + 4(-3|(1((-2x - 3)/(-3x + 4))^2 + 3((-2x - 3)/(-3x + 4)) - 2) + 3| + 2)) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "419", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(2e^(-1((1(-1|(-1x + 2) - 3| + 2) - 2)/(3(-1|(-1x + 2) - 3| + 2) + 1))) - 3) + 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((1(-1sin(2\u03c0(-1(-3x) - 2) - 3)) - 3)/(-2(-1sin(2\u03c0(-1(-3x) - 2) - 3)) - 2)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0(-1|((-3(4((1x - 3)/(2x - 1))) - 2)/(3(4((1x - 3)/(2x - 1))))) - 1| - 3)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(2((2(2(-2sin(2\u03c0x - 2) + 1) - 5))/(2(2(-2sin(2\u03c0x - 2) + 1) - 5) - 3)) + 2)^2 + 1(2((2(2(-2sin(2\u03c0x - 2) + 1) - 5))/(2(2(-2sin(2\u03c0x - 2) + 1) - 5) - 3)) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-2(-1(-2|(3x^2 - 5x - 3) + 3| + 3) + 4)^2 + 5(-1(-2|(3x^2 - 5x - 3) + 3| + 3) + 4) + 3) + 1)/(-1(-2(-1(-2|(3x^2 - 5x - 3) + 3| + 3) + 4)^2 + 5(-1(-2|(3x^2 - 5x - 3) + 3| + 3) + 4) + 3) + 2) where -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 number of x-intercepts of the function f(x) = 1((-2(-1(-3(-2|x + 1| + 1)^2) - 1) + 1)/(2(-1(-3(-2|x + 1| + 1)^2) - 1) + 1)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(1|(2(1(1|x - 2|)^2 - 5(1|x - 2|) + 5)^2 + 3(1(1|x - 2|)^2 - 5(1|x - 2|) + 5) - 1) + 3| + 1) + 3)/(1(1|(2(1(1|x - 2|)^2 - 5(1|x - 2|) + 5)^2 + 3(1(1|x - 2|)^2 - 5(1|x - 2|) + 5) - 1) + 3| + 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(4(-4(3sin(3\u03c0(5x + 3) - 3) + 3) + 2)^2 + 2(-4(3sin(3\u03c0(5x + 3) - 3) + 3) + 2) - 3)^2 - 2(4(-4(3sin(3\u03c0(5x + 3) - 3) + 3) + 2)^2 + 2(-4(3sin(3\u03c0(5x + 3) - 3) + 3) + 2) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(1\u03c0(-4(-1(-4(1x - 1)) + 2)^2) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1152", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(-3|(2(2|((2x + 1)/(1x - 3)) - 1| + 1) + 3) - 1| + 2) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "325", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2|((3(-5(2cos(2\u03c0x - 2) + 2)^2 - 3(2cos(2\u03c0x - 2) + 2)) + 1)/(2(-5(2cos(2\u03c0x - 2) + 2)^2 - 3(2cos(2\u03c0x - 2) + 2)) + 2)) + 1| - 1)^2 - 4(-2|((3(-5(2cos(2\u03c0x - 2) + 2)^2 - 3(2cos(2\u03c0x - 2) + 2)) + 1)/(2(-5(2cos(2\u03c0x - 2) + 2)^2 - 3(2cos(2\u03c0x - 2) + 2)) + 2)) + 1| - 1) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-4(-2cos(2\u03c0(-5(3x^2 + 2x) + 3)) + 1) + 5) + 3)/(-2(-4(-2cos(2\u03c0(-5(3x^2 + 2x) + 3)) + 1) + 5) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "734", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((2(2sin(2\u03c0(1((1x + 1)/(1x - 2))^2 - 3((1x + 1)/(1x - 2)) - 4) + 3) - 1) + 3)/(1(2sin(2\u03c0(1((1x + 1)/(1x - 2))^2 - 3((1x + 1)/(1x - 2)) - 4) + 3) - 1) - 3)) + 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "225", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(-1(-4(3|((-2x + 3)/(1x + 3)) - 1| - 1)^2 + 2(3|((-2x + 3)/(1x + 3)) - 1| - 1) - 4)^2 - 2(-4(3|((-2x + 3)/(1x + 3)) - 1| - 1)^2 + 2(3|((-2x + 3)/(1x + 3)) - 1| - 1) - 4) + 4) - 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "869", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2((-1(4(-3|(1x - 3) - 3| + 3)^2 - 2(-3|(1x - 3) - 3| + 3)) + 2)/(-2(4(-3|(1x - 3) - 3| + 3)^2 - 2(-3|(1x - 3) - 3| + 3)) + 3)) + 2)/(2((-1(4(-3|(1x - 3) - 3| + 3)^2 - 2(-3|(1x - 3) - 3| + 3)) + 2)/(-2(4(-3|(1x - 3) - 3| + 3)^2 - 2(-3|(1x - 3) - 3| + 3)) + 3)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-4(2(-4(-1cos(1\u03c0x - 1))^2 - 3(-1cos(1\u03c0x - 1)) - 1)^2 + 1(-4(-1cos(1\u03c0x - 1))^2 - 3(-1cos(1\u03c0x - 1)) - 1) - 5) - 5) - 3)/(3(-4(2(-4(-1cos(1\u03c0x - 1))^2 - 3(-1cos(1\u03c0x - 1)) - 1)^2 + 1(-4(-1cos(1\u03c0x - 1))^2 - 3(-1cos(1\u03c0x - 1)) - 1) - 5) - 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(1\u03c0(-4(5(-5(5x^2 + 5x + 5)^2 + 5(5x^2 + 5x + 5) + 5) - 1) + 3) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "368", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(1\u03c0(-1(1(-4((2x + 1)/(-3x + 4)) + 3) - 1)^2 + 3(1(-4((2x + 1)/(-3x + 4)) + 3) - 1) - 3)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(3sin(3\u03c0(2(-4(-4x^2 + 5x + 5)^2 - 3(-4x^2 + 5x + 5) + 3) + 5) - 1) + 3)^2 + 4(3sin(3\u03c0(2(-4(-4x^2 + 5x + 5)^2 - 3(-4x^2 + 5x + 5) + 3) + 5) - 1) + 3) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "382", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-1(1(1|(2x^2 - 5x - 3) + 1| - 3)^2 - 3(1|(2x^2 - 5x - 3) + 1| - 3) - 3) + 5) + 1)/(1(-1(1(1|(2x^2 - 5x - 3) + 1| - 3)^2 - 3(1|(2x^2 - 5x - 3) + 1| - 3) - 3) + 5) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((-2(-2|(-4(-1x^2 - 2x + 1) - 2)| + 2) - 1)/(-2(-2|(-4(-1x^2 - 2x + 1) - 2)| + 2) - 2))^2 - 1((-2(-2|(-4(-1x^2 - 2x + 1) - 2)| + 2) - 1)/(-2(-2|(-4(-1x^2 - 2x + 1) - 2)| + 2) - 2)) have 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 number of x-intercepts of the function f(x) = (-2((-3(2sin(3\u03c0(4(-1|x - 3| + 1) + 2) + 2) + 3))/(2(2sin(3\u03c0(4(-1|x - 3| + 1) + 2) + 2) + 3) + 3)) - 2)/(2((-3(2sin(3\u03c0(4(-1|x - 3| + 1) + 2) + 2) + 3))/(2(2sin(3\u03c0(4(-1|x - 3| + 1) + 2) + 2) + 3) + 3)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-4(2|(1|(5x^2 - 3x - 4) - 2| - 3) - 1| - 3) + 4) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1((-1(-1(1(1e^(-2x) + 3)^2 - 3) - 1) + 2)/(-1(-1(1(1e^(-2x) + 3)^2 - 3) - 1) - 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "61", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(-3|(-1|(-4(-3|x + 3| + 1)^2 - 1(-3|x + 3| + 1) - 2)| + 3) + 1| - 3) + 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1425", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(1((2(-2|(1cos(1\u03c0x - 1) + 1)| + 1) + 1)/(1(-2|(1cos(1\u03c0x - 1) + 1)| + 1) + 1)) - 3) + 3)/(-3(1((2(-2|(1cos(1\u03c0x - 1) + 1)| + 1) + 1)/(1(-2|(1cos(1\u03c0x - 1) + 1)| + 1) + 1)) - 3) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0(3|(-1(-3(-1|x + 2| - 2)^2 + 4(-1|x + 2| - 2) + 2)^2 + 2(-3(-1|x + 2| - 2)^2 + 4(-1|x + 2| - 2) + 2) - 5) - 2| - 1) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "564", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(1sin(2\u03c0(5(-3|(5x - 5)| - 1)^2 - 4(-3|(5x - 5)| - 1) + 3) + 1) + 2) + 2)/(-1(1sin(2\u03c0(5(-3|(5x - 5)| - 1)^2 - 4(-3|(5x - 5)| - 1) + 3) + 1) + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1453", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0(1|(-1(2|(-1|x - 3| + 2) - 2| + 1)^2 + 2(2|(-1|x - 3| + 2) - 2| + 1) + 5) + 1| - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "871", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2e^(1(-3|(2(3(3x^2 - 5x - 4)^2 + 1(3x^2 - 5x - 4) + 2) - 1) - 3| + 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-4(-2sin(3\u03c0((3(-4x^2 + 3) - 3)/(1(-4x^2 + 3) + 1)) - 1) + 1) + 1) + 3)/(-3(-4(-2sin(3\u03c0((3(-4x^2 + 3) - 3)/(1(-4x^2 + 3) + 1)) - 1) + 1) + 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1|((-2(-1cos(3\u03c0(-4x + 3) + 1)) + 3)/(1(-1cos(3\u03c0(-4x + 3) + 1)))) + 1| + 3) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "112", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0((1(2|((-2((-1x + 2)/(-2x + 3)) + 2)/(3((-1x + 2)/(-2x + 3)) + 1)) + 3| - 3) + 1)/(1(2|((-2((-1x + 2)/(-2x + 3)) + 2)/(3((-1x + 2)/(-2x + 3)) + 1)) + 3| - 3) + 2)) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(-4((-3(-1|(-3|x - 1|) + 2| + 1) + 3)/(3(-1|(-3|x - 1|) + 2| + 1) - 2)) + 1) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2e^(-2(1|(5((3(-2x + 5))/(-2(-2x + 5) - 3))^2 - 5((3(-2x + 5))/(-2(-2x + 5) - 3)) - 5) - 2| + 2)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5((-2(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 2) - 3)/(1(-5(2sin(1\u03c0(-1x^2 - 3x - 2) + 1) - 1) + 2))) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "186", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(2cos(2\u03c0((-3(-1|(-1x + 4)|) - 3)/(2(-1|(-1x + 4)|) + 1)) - 2) + 1)^2 - 2(2cos(2\u03c0((-3(-1|(-1x + 4)|) - 3)/(2(-1|(-1x + 4)|) + 1)) - 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(2\u03c0(5(2|(2(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 2) + 4) - 3| + 1)^2 + 3(2|(2(-2|x - 1| + 2)^2 - 2(-2|x - 1| + 2) + 4) - 3| + 1) + 4) - 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "370", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-1(1(-4(2sin(1\u03c0x + 2) + 2) + 5) + 2) + 3)/(-3(1(-4(2sin(1\u03c0x + 2) + 2) + 5) + 2))) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-3(-2(-1|(-1x^2 - 5x + 1) - 2| + 1)^2 + 3(-1|(-1x^2 - 5x + 1) - 2| + 1) + 2) + 5) - 1)/(1(-3(-2(-1|(-1x^2 - 5x + 1) - 2| + 1)^2 + 3(-1|(-1x^2 - 5x + 1) - 2| + 1) + 2) + 5) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-3(-2sin(2\u03c0(1(-3x^2 + 4x)^2 - 2(-3x^2 + 4x) + 1) + 2) + 2) + 5) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "847", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(1|(-2|((2(4x^2 + 3x - 4) - 2)/(1(4x^2 + 3x - 4) + 2)) + 3| + 2) + 3| - 3))/(2(1|(-2|((2(4x^2 + 3x - 4) - 2)/(1(4x^2 + 3x - 4) + 2)) + 3| + 2) + 3| - 3) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(1\u03c0(-5(-5(-1|((1x - 1)/(-2x + 1)) - 3| - 3)^2 + 5)) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((2((1(-3cos(1\u03c0(5x^2 + 4x + 4))) + 2)/(-1(-3cos(1\u03c0(5x^2 + 4x + 4))) + 3)) - 2)/(3((1(-3cos(1\u03c0(5x^2 + 4x + 4))) + 2)/(-1(-3cos(1\u03c0(5x^2 + 4x + 4))) + 3)) - 2)) + 3)/(1((2((1(-3cos(1\u03c0(5x^2 + 4x + 4))) + 2)/(-1(-3cos(1\u03c0(5x^2 + 4x + 4))) + 3)) - 2)/(3((1(-3cos(1\u03c0(5x^2 + 4x + 4))) + 2)/(-1(-3cos(1\u03c0(5x^2 + 4x + 4))) + 3)) - 2)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(2(1(-3sin(3\u03c0(3x^2 + 5) + 1) + 3)^2 - 3(-3sin(3\u03c0(3x^2 + 5) + 1) + 3) + 1)^2 - 4(1(-3sin(3\u03c0(3x^2 + 5) + 1) + 3)^2 - 3(-3sin(3\u03c0(3x^2 + 5) + 1) + 3) + 1) - 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "937", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(3((-1(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1) + 2)/(3(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1)))^2 + 1((-1(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1) + 2)/(3(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1))) - 3) + 3)/(-1(3((-1(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1) + 2)/(3(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1)))^2 + 1((-1(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1) + 2)/(3(-3(-2e^(-2x) + 2)^2 + 1(-2e^(-2x) + 2) + 1))) - 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(2(2|(1cos(2\u03c0(-1|x + 1| - 2) + 2)) - 2| - 3) - 1) - 1| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(1(3(-2|(1|x + 3| + 1) - 3| + 1)^2 - 1(-2|(1|x + 3| + 1) - 3| + 1) - 4) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(1(1(-3(1x - 3)^2 - 4(1x - 3))^2 + 2(-3(1x - 3)^2 - 4(1x - 3)) - 3)^2 - 3(1(-3(1x - 3)^2 - 4(1x - 3))^2 + 2(-3(1x - 3)^2 - 4(1x - 3)) - 3) - 3)^2 - 4(1(1(-3(1x - 3)^2 - 4(1x - 3))^2 + 2(-3(1x - 3)^2 - 4(1x - 3)) - 3)^2 - 3(1(-3(1x - 3)^2 - 4(1x - 3))^2 + 2(-3(1x - 3)^2 - 4(1x - 3)) - 3) - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-2sin(3\u03c0((2((2((-2x + 3)/(3x - 2)) - 2)/(-2((-2x + 3)/(3x - 2)) + 3)) + 1)/(1((2((-2x + 3)/(3x - 2)) - 2)/(-2((-2x + 3)/(3x - 2)) + 3)) - 2))) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(3e^(2(-4(1(-2x^2 - 3x + 5)^2 - 5(-2x^2 - 3x + 5) - 4)^2 + 4(1(-2x^2 - 3x + 5)^2 - 5(-2x^2 - 3x + 5) - 4) - 2)) - 3) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3((3(-5(-5(-1x^2 - 2x + 1) + 4)^2 + 3(-5(-1x^2 - 2x + 1) + 4)) + 1)/(3(-5(-5(-1x^2 - 2x + 1) + 4)^2 + 3(-5(-1x^2 - 2x + 1) + 4)) - 2)) + 1)/(2((3(-5(-5(-1x^2 - 2x + 1) + 4)^2 + 3(-5(-1x^2 - 2x + 1) + 4)) + 1)/(3(-5(-5(-1x^2 - 2x + 1) + 4)^2 + 3(-5(-1x^2 - 2x + 1) + 4)) - 2)) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-2((3(-2|(-2x^2 + 2x - 2) + 1| + 2) + 3)/(1(-2|(-2x^2 + 2x - 2) + 1| + 2)))^2 + 1((3(-2|(-2x^2 + 2x - 2) + 1| + 2) + 3)/(1(-2|(-2x^2 + 2x - 2) + 1| + 2))) + 1))/(-3(-2((3(-2|(-2x^2 + 2x - 2) + 1| + 2) + 3)/(1(-2|(-2x^2 + 2x - 2) + 1| + 2)))^2 + 1((3(-2|(-2x^2 + 2x - 2) + 1| + 2) + 3)/(1(-2|(-2x^2 + 2x - 2) + 1| + 2))) + 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(5(2cos(1\u03c0(4(-3|x + 3| - 3)^2 + 2(-3|x + 3| - 3)) - 1) + 1) - 1) + 3| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "540", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(3sin(3\u03c0(-2(-2(-1x - 5) - 1)^2 + 4(-2(-1x - 5) - 1) + 3) - 3) + 1) + 1)/(2(3sin(3\u03c0(-2(-2(-1x - 5) - 1)^2 + 4(-2(-1x - 5) - 1) + 3) - 3) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1054", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(-2(-4(2|(3|x - 3| - 2) - 2| - 2)^2 + 4(2|(3|x - 3| - 2) - 2| - 2))^2 + 1(-4(2|(3|x - 3| - 2) - 2| - 2)^2 + 4(2|(3|x - 3| - 2) - 2| - 2)) + 3) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(1|(-3|(3|(3x^2 - 2x + 2) - 2| + 1) - 1| - 3) + 3|) + 1)/(3(1|(-3|(3|(3x^2 - 2x + 2) - 2| + 1) - 1| - 3) + 3|) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-2cos(1\u03c0(1(3|(4x + 3) - 3| - 2)^2 + 4(3|(4x + 3) - 3| - 2) + 5) + 3) - 1) + 1| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "921", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(2sin(2\u03c0(2|((1(2x^2 - 4x - 4) - 3)/(-1(2x^2 - 4x - 4) - 3)) - 1| + 1) + 2) - 1) + 1)/(-2(2sin(2\u03c0(2|((1(2x^2 - 4x - 4) - 3)/(-1(2x^2 - 4x - 4) - 3)) - 1| + 1) + 2) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "86", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1(3sin(3\u03c0(2(3x - 3)^2 - 2(3x - 3) - 5)) - 2) - 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1142", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-3cos(3\u03c0(-5(-2(-5x - 5) - 3) - 2)) + 1) + 1)/(1(-3cos(3\u03c0(-5(-2(-5x - 5) - 3) - 2)) + 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "426", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(1sin(2\u03c0(-4(3|(-1x + 2) + 3| - 2)^2 + 2(3|(-1x + 2) + 3| - 2) - 4) + 3) + 2)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1088", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(3(3|(1|(3x^2 - 1x - 4) - 2| - 1) - 2|)^2) + 2)/(-3(3(3|(1|(3x^2 - 1x - 4) - 2| - 1) - 2|)^2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1(2(2|((-1x - 2)/(-2x + 3)) - 3| + 1)^2 - 3(2|((-1x - 2)/(-2x + 3)) - 3| + 1) - 2)^2 - 5(2(2|((-1x - 2)/(-2x + 3)) - 3| + 1)^2 - 3(2|((-1x - 2)/(-2x + 3)) - 3| + 1) - 2) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(1|(2|(2((-2x - 3)/(3x - 2)))|) + 3|) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2((1(-4(2sin(2\u03c0(-4x^2 - 1x - 3) - 1))^2 - 5(2sin(2\u03c0(-4x^2 - 1x - 3) - 1)) + 1) - 3)/(3(-4(2sin(2\u03c0(-4x^2 - 1x - 3) - 1))^2 - 5(2sin(2\u03c0(-4x^2 - 1x - 3) - 1)) + 1) - 2))^2 + 2((1(-4(2sin(2\u03c0(-4x^2 - 1x - 3) - 1))^2 - 5(2sin(2\u03c0(-4x^2 - 1x - 3) - 1)) + 1) - 3)/(3(-4(2sin(2\u03c0(-4x^2 - 1x - 3) - 1))^2 - 5(2sin(2\u03c0(-4x^2 - 1x - 3) - 1)) + 1) - 2)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "548", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1((3(-2cos(1\u03c0(-1(2|x + 3| - 3) + 4) - 2)))/(-2(-2cos(1\u03c0(-1(2|x + 3| - 3) + 4) - 2)) - 1))^2 + 1((3(-2cos(1\u03c0(-1(2|x + 3| - 3) + 4) - 2)))/(-2(-2cos(1\u03c0(-1(2|x + 3| - 3) + 4) - 2)) - 1)) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(3|(-3|(-2(-2cos(3\u03c0x - 3) + 1) + 4) - 2|) + 1| - 1)^2 - 3(3|(-3|(-2(-2cos(3\u03c0x - 3) + 1) + 4) - 2|) + 1| - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(5(-3sin(1\u03c0((-2(-2x^2 - 3x - 5) - 2)/(-1(-2x^2 - 3x - 5) - 3)) + 3) - 1)) + 3)/(-3(5(-3sin(1\u03c0((-2(-2x^2 - 3x - 5) - 2)/(-1(-2x^2 - 3x - 5) - 3)) + 3) - 1)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-1e^(1((2(-5(-1|x + 2| + 2)^2 + 3(-1|x + 2| + 2) + 2) + 2)/(-2(-5(-1|x + 2| + 2)^2 + 3(-1|x + 2| + 2) + 2) - 1))) + 3) - 3 have 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 number of x-intercepts of the function f(x) = -1(-2|(-3(3|(2|x + 1| - 3) - 1|) + 3) + 2| - 2)^2 - 4(-2|(-3(3|(2|x + 1| - 3) - 1|) + 3) + 2| - 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-3(1|(2(-3|x + 3| + 3) + 4) - 1| - 2) - 1) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1e^(2(-1(-3(1(-2x + 3)^2 + 2(-2x + 3) - 1)^2 - 4(1(-2x + 3)^2 + 2(-2x + 3) - 1) + 1) - 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0(1(-2(4(2x^2 - 1x + 1)^2 + 3(2x^2 - 1x + 1) - 2) - 5) + 2) + 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1173", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(2|(4(-3|(4x^2 - 1x - 3) + 2| + 2) + 3) - 2| - 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-1(1(3|((2x + 3)/(-2x - 2)) + 1| - 2)^2 - 3)^2 - 5(1(3|((2x + 3)/(-2x - 2)) + 1| - 2)^2 - 3)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(-2cos(3\u03c0(1|(-2|((-2x - 1)/(-3x - 3)) - 1| + 3)| - 1) + 3) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(4((3(-4(1|x - 2| - 3)))/(-1(-4(1|x - 2| - 3)) - 1))^2 + 1((3(-4(1|x - 2| - 3)))/(-1(-4(1|x - 2| - 3)) - 1)) + 5)^2 + 4(4((3(-4(1|x - 2| - 3)))/(-1(-4(1|x - 2| - 3)) - 1))^2 + 1((3(-4(1|x - 2| - 3)))/(-1(-4(1|x - 2| - 3)) - 1)) + 5) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(1((1(-1(-3sin(1\u03c0x - 1) + 1)^2 + 3(-3sin(1\u03c0x - 1) + 1)) - 3)/(-1(-1(-3sin(1\u03c0x - 1) + 1)^2 + 3(-3sin(1\u03c0x - 1) + 1)) - 2))^2 - 2((1(-1(-3sin(1\u03c0x - 1) + 1)^2 + 3(-3sin(1\u03c0x - 1) + 1)) - 3)/(-1(-1(-3sin(1\u03c0x - 1) + 1)^2 + 3(-3sin(1\u03c0x - 1) + 1)) - 2)) - 3) + 3| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(2sin(2\u03c0(-2(1|((2x - 3)/(3x + 1)) + 1| + 2)^2 + 4(1|((2x - 3)/(3x + 1)) + 1| + 2) - 1)) - 2))/(-2(2sin(2\u03c0(-2(1|((2x - 3)/(3x + 1)) + 1| + 2)^2 + 4(1|((2x - 3)/(3x + 1)) + 1| + 2) - 1)) - 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "123", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1(-1sin(2\u03c0(-2|(-5x + 1) + 3|) + 3) - 3)^2 - 3(-1sin(2\u03c0(-2|(-5x + 1) + 3|) + 3) - 3) + 3) - 3)/(2(-1(-1sin(2\u03c0(-2|(-5x + 1) + 3|) + 3) - 3)^2 - 3(-1sin(2\u03c0(-2|(-5x + 1) + 3|) + 3) - 3) + 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "399", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-1|(2sin(2\u03c0(3|(2x)| - 1) - 1) + 3) - 2| + 1) - 3)/(-1(-1|(2sin(2\u03c0(3|(2x)| - 1) - 1) + 3) - 2| + 1) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-2|(2|((-3(-5x + 2) - 1)/(-1(-5x + 2) + 3)) + 3| - 2) + 1| + 3) + 1| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(2|((2((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) + 1)/(-3((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) - 1))| - 3)^2 - 2(2|((2((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) + 1)/(-3((1(-2x^2 + 4) + 2)/(2(-2x^2 + 4) + 1)) - 1))| - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(3\u03c0(2(-3((-2(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) - 1))^2 - 2((-2(-2|x - 3| + 3) + 1)/(-1(-2|x - 3| + 3) - 1)) - 1) + 5) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "569", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3((2(-5(1x^2 - 3x - 5) - 2))/(-2(-5(1x^2 - 3x - 5) - 2) + 3))^2 + 5((2(-5(1x^2 - 3x - 5) - 2))/(-2(-5(1x^2 - 3x - 5) - 2) + 3))) + 3)/(3(3((2(-5(1x^2 - 3x - 5) - 2))/(-2(-5(1x^2 - 3x - 5) - 2) + 3))^2 + 5((2(-5(1x^2 - 3x - 5) - 2))/(-2(-5(1x^2 - 3x - 5) - 2) + 3))) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(5(-2(-1|(-1|x + 1| + 1) + 3| + 1)^2 + 4(-1|(-1|x + 1| + 1) + 3| + 1) + 4) + 2) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(3cos(3\u03c0(-3|((-2(-1x - 3) + 1)/(2(-1x - 3))) + 2| - 3) - 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-2|(4(-5(-2|x - 2|) - 3)^2 - 1(-5(-2|x - 2|) - 3) - 1) - 2| + 3) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-1(3(5((1x + 1)/(-1x - 3))^2 - 1((1x + 1)/(-1x - 3)) - 4) + 1)^2 + 5(3(5((1x + 1)/(-1x - 3))^2 - 1((1x + 1)/(-1x - 3)) - 4) + 1) + 3) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(1(3|(-3(-3e^(2x))^2 - 2(-3e^(2x)) + 5) + 2| - 2)^2 - 5(3|(-3(-3e^(2x))^2 - 2(-3e^(2x)) + 5) + 2| - 2) + 5) - 2| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(1(-2(-2(-1x + 3)^2 - 4(-1x + 3) + 2)^2 - 5(-2(-1x + 3)^2 - 4(-1x + 3) + 2) + 1)^2 - 3(-2(-2(-1x + 3)^2 - 4(-1x + 3) + 2)^2 - 5(-2(-1x + 3)^2 - 4(-1x + 3) + 2) + 1) + 4) + 5 have 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 number of x-intercepts of the function f(x) = -2|(5(-1|(-2cos(3\u03c0((-1x + 1)/(-3x - 1)) + 1) - 1) - 1| + 1) + 1)| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0((1((1(3(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3) + 2)/(3(3(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3) + 1)) + 2)/(-2((1(3(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3) + 2)/(3(3(2|x + 3| + 1)^2 - 4(2|x + 3| + 1) - 3) + 1)) + 1)) + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(-5(5(-3((-2x + 2)/(2x - 3)) - 2)) - 2) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "130", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-2|(1|(1(-1x^2 - 5x - 4)^2 - 2(-1x^2 - 5x - 4) - 3) + 1|) - 3|)^2 + 5(-2|(1|(1(-1x^2 - 5x - 4)^2 - 2(-1x^2 - 5x - 4) - 3) + 1|) - 3|) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((-2(-1|(-2|(-1cos(1\u03c0x + 1) + 1) - 1| - 3)| + 3) - 2)/(-3(-1|(-2|(-1cos(1\u03c0x + 1) + 1) - 1| - 3)| + 3) - 1)) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-3(4(-2|(2x) + 2|))^2 - 1(4(-2|(2x) + 2|)) + 2)^2 + 1(-3(4(-2|(2x) + 2|))^2 - 1(4(-2|(2x) + 2|)) + 2) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-3|(2cos(3\u03c0(-2|((2x - 2)/(-2x - 1)) - 2| + 3) - 2) - 1) + 1|)^2 - 3(-3|(2cos(3\u03c0(-2|((2x - 2)/(-2x - 1)) - 2| + 3) - 2) - 1) + 1|) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "118", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((1((1(1(-2|x - 2| - 1)^2 + 3(-2|x - 2| - 1)) + 2)/(-1(1(-2|x - 2| - 1)^2 + 3(-2|x - 2| - 1)) + 2)) - 3)/(-2((1(1(-2|x - 2| - 1)^2 + 3(-2|x - 2| - 1)) + 2)/(-1(1(-2|x - 2| - 1)^2 + 3(-2|x - 2| - 1)) + 2)))) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(3|(3((3((2x - 2)/(3x + 3)) - 3)/(-3((2x - 2)/(3x + 3)) - 1))^2 + 4((3((2x - 2)/(3x + 3)) - 3)/(-3((2x - 2)/(3x + 3)) - 1)) + 1)| + 1) - 3)/(1(3|(3((3((2x - 2)/(3x + 3)) - 3)/(-3((2x - 2)/(3x + 3)) - 1))^2 + 4((3((2x - 2)/(3x + 3)) - 3)/(-3((2x - 2)/(3x + 3)) - 1)) + 1)| + 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1|((-1(-1|(-4x - 1) - 1| + 3) + 3)/(3(-1|(-4x - 1) - 1| + 3))) + 1| + 2)^2 - 3(-1|((-1(-1|(-4x - 1) - 1| + 3) + 3)/(3(-1|(-4x - 1) - 1| + 3))) + 1| + 2) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(-4(4(-3sin(1\u03c0(-5x^2 - 4x + 1) - 1) + 3) - 5) + 1) - 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(1|(2sin(1\u03c0(5(-1|x + 2|)^2 + 1(-1|x + 2|) + 2) + 2) - 1) - 3| - 3)^2 - 5(1|(2sin(1\u03c0(5(-1|x + 2|)^2 + 1(-1|x + 2|) + 2) + 2) - 1) - 3| - 3) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1001", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(1\u03c0((-3(-3|(3(-3|x + 2| + 1)^2 + 1(-3|x + 2| + 1) + 1)| + 1) + 2)/(-3(-3|(3(-3|x + 2| + 1)^2 + 1(-3|x + 2| + 1) + 1)| + 1) + 1)) - 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|((2(2((-2(-2sin(1\u03c0x - 2) - 1) - 3)/(-2(-2sin(1\u03c0x - 2) - 1) + 3)) + 4) - 3)/(-2(2((-2(-2sin(1\u03c0x - 2) - 1) - 3)/(-2(-2sin(1\u03c0x - 2) - 1) + 3)) + 4) - 2))| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(2\u03c0(2((3((-2((3x + 2)/(-1x - 1)))/(2((3x + 2)/(-1x - 1)) - 3)) + 1)/(-2((-2((3x + 2)/(-1x - 1)))/(2((3x + 2)/(-1x - 1)) - 3)))) + 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-3(-1((-2((3x - 3)/(2x - 3)) - 1)/(2((3x - 3)/(2x - 3)) - 3))^2 + 2)^2 - 3(-1((-2((3x - 3)/(2x - 3)) - 1)/(2((3x - 3)/(2x - 3)) - 3))^2 + 2) + 5) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(3cos(1\u03c0(3(-1|(-2|x - 1| + 3) + 3| - 2) - 5) - 3) - 1) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(2|(2|((3((3x + 3)/(-2x + 3)) + 1)/(3((3x + 3)/(-2x + 3)) - 2)) + 1| - 1) - 3|)^2 + 5(2|(2|((3((3x + 3)/(-2x + 3)) + 1)/(3((3x + 3)/(-2x + 3)) - 2)) + 1| - 1) - 3|) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(3(-3sin(3\u03c0(1|(-2x^2 + 2) - 2| + 2) - 2))^2 + 4(-3sin(3\u03c0(1|(-2x^2 + 2) - 2| + 2) - 2)) - 4) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1382", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2e^(-2(1|((-2(-1(1|x - 2| - 3)) + 1)/(1(-1(1|x - 2| - 3)) + 3))| - 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(4((-1(-4(-1x^2 + 1x + 4)^2 + 3) - 1)/(1(-4(-1x^2 + 1x + 4)^2 + 3) + 3)) - 5)^2 - 3(4((-1(-4(-1x^2 + 1x + 4)^2 + 3) - 1)/(1(-4(-1x^2 + 1x + 4)^2 + 3) + 3)) - 5) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2|(4((-3(2(-1x^2 - 4x + 1)^2 + 3(-1x^2 - 4x + 1) - 3) - 1)/(2(2(-1x^2 - 4x + 1)^2 + 3(-1x^2 - 4x + 1) - 3) - 1)) - 3) - 1| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3((-3(-2|(1sin(1\u03c0(-2x)) + 1) - 1| - 3) - 3)/(2(-2|(1sin(1\u03c0(-2x)) + 1) - 1| - 3) - 3))^2 + 4((-3(-2|(1sin(1\u03c0(-2x)) + 1) - 1| - 3) - 3)/(2(-2|(1sin(1\u03c0(-2x)) + 1) - 1| - 3) - 3)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(2\u03c0(-2|(5(-4(-2|x - 2| - 2)^2 + 1(-2|x - 2| - 2) + 5) + 2) + 1| - 1) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1288", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-3(3cos(2\u03c0(2|(-3|x - 3| - 1) - 3| - 3) + 3) - 1)^2 + 1(3cos(2\u03c0(2|(-3|x - 3| - 1) - 3| - 3) + 3) - 1) + 1) + 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "245", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(3\u03c0((-1((3(-2(-1|x + 1| - 1)^2 - 2(-1|x + 1| - 1) + 2) - 1)/(2(-2(-1|x + 1| - 1)^2 - 2(-1|x + 1| - 1) + 2))) + 3)/(2((3(-2(-1|x + 1| - 1)^2 - 2(-1|x + 1| - 1) + 2) - 1)/(2(-2(-1|x + 1| - 1)^2 - 2(-1|x + 1| - 1) + 2)))))) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4((3((-1((-1(-2cos(3\u03c0x - 2) + 2) + 2)/(-3(-2cos(3\u03c0x - 2) + 2) + 1)) - 1)/(2((-1(-2cos(3\u03c0x - 2) + 2) + 2)/(-3(-2cos(3\u03c0x - 2) + 2) + 1)) - 1)) - 2)/(-3((-1((-1(-2cos(3\u03c0x - 2) + 2) + 2)/(-3(-2cos(3\u03c0x - 2) + 2) + 1)) - 1)/(2((-1(-2cos(3\u03c0x - 2) + 2) + 2)/(-3(-2cos(3\u03c0x - 2) + 2) + 1)) - 1)) - 2))^2 - 4((3((-1((-1(-2cos(3\u03c0x - 2) + 2) + 2)/(-3(-2cos(3\u03c0x - 2) + 2) + 1)) - 1)/(2((-1(-2cos(3\u03c0x - 2) + 2) + 2)/(-3(-2cos(3\u03c0x - 2) + 2) + 1)) - 1)) - 2)/(-3((-1((-1(-2cos(3\u03c0x - 2) + 2) + 2)/(-3(-2cos(3\u03c0x - 2) + 2) + 1)) - 1)/(2((-1(-2cos(3\u03c0x - 2) + 2) + 2)/(-3(-2cos(3\u03c0x - 2) + 2) + 1)) - 1)) - 2)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1(-1sin(1\u03c0(-1(5x + 3) + 3)) + 3) + 3) - 2)/(3(-1(-1sin(1\u03c0(-1(5x + 3) + 3)) + 3) + 3) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(3\u03c0(3((2((-1(-4x + 2) + 3)/(1(-4x + 2) + 2)) + 2)/(2((-1(-4x + 2) + 3)/(1(-4x + 2) + 2)) - 3)) - 5) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "75", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(3(-1(-2(-5x^2 + 3)^2 - 2)^2 + 5) - 4)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-3(3sin(1\u03c0(-5((1x + 1)/(-1x + 2))^2 + 5((1x + 1)/(-1x + 2)) + 2) + 1) + 3) + 2)| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(1(3(-1sin(3\u03c0(2|x + 3| + 3) - 3) - 2)^2 + 5(-1sin(3\u03c0(2|x + 3| + 3) - 3) - 2) - 2)^2 - 4(3(-1sin(3\u03c0(2|x + 3| + 3) - 3) - 2)^2 + 5(-1sin(3\u03c0(2|x + 3| + 3) - 3) - 2) - 2))^2 + 4(1(3(-1sin(3\u03c0(2|x + 3| + 3) - 3) - 2)^2 + 5(-1sin(3\u03c0(2|x + 3| + 3) - 3) - 2) - 2)^2 - 4(3(-1sin(3\u03c0(2|x + 3| + 3) - 3) - 2)^2 + 5(-1sin(3\u03c0(2|x + 3| + 3) - 3) - 2) - 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "339", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-4(2|(2((3x)/(2x - 1))^2 - 5((3x)/(2x - 1))) + 2| - 3) - 5)^2 + 5(-4(2|(2((3x)/(2x - 1))^2 - 5((3x)/(2x - 1))) + 2| - 3) - 5) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-1(4(-3(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) + 3) - 4)^2 - 3(4(-3(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) + 3) - 4) + 5))/(1(-1(4(-3(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) + 3) - 4)^2 - 3(4(-3(1|x - 1| - 1)^2 - 4(1|x - 1| - 1) + 3) - 4) + 5) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(1cos(1\u03c0(5(1|(-3x - 3) - 2| + 1) + 3)) - 1) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(-1|(-4(-1cos(2\u03c0((1x - 3)/(2x + 3)) + 3) + 2)^2 + 5(-1cos(2\u03c0((1x - 3)/(2x + 3)) + 3) + 2) - 1)| + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1|(-1|(-1|(3x^2 + 2x - 2) - 2| - 1) + 1| - 2) + 1| + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(2cos(3\u03c0((1(-1((1x - 3)/(-1x - 2))^2 - 4((1x - 3)/(-1x - 2)) - 3) + 3)/(2(-1((1x - 3)/(-1x - 2))^2 - 4((1x - 3)/(-1x - 2)) - 3) + 2)) - 2) + 3) - 3| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(2(-1sin(1\u03c0(4(3|x - 3| - 2) + 4)) + 2)^2 - 5(-1sin(1\u03c0(4(3|x - 3| - 2) + 4)) + 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-2|(-2|(3sin(3\u03c0(1|x + 1| - 3) - 2) + 1) - 3| + 2) + 3| - 2) + 2| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(1\u03c0(-2|(-1(1|(5x + 2) + 2|) + 2) - 3| - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-4((2(-1cos(2\u03c0(2x + 5) + 3) + 1) + 1)/(3(-1cos(2\u03c0(2x + 5) + 3) + 1) + 2))) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-2(-1((-2((1x)/(2x - 3)) + 2)/(3((1x)/(2x - 3)) - 2))^2 - 5((-2((1x)/(2x - 3)) + 2)/(3((1x)/(2x - 3)) - 2)) + 4) - 1)^2 + 5(-2(-1((-2((1x)/(2x - 3)) + 2)/(3((1x)/(2x - 3)) - 2))^2 - 5((-2((1x)/(2x - 3)) + 2)/(3((1x)/(2x - 3)) - 2)) + 4) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1((1((-1(-1cos(1\u03c0((-2x + 2)/(2x + 3)) - 1) - 1))/(-3(-1cos(1\u03c0((-2x + 2)/(2x + 3)) - 1) - 1) - 2)) + 3)/(3((-1(-1cos(1\u03c0((-2x + 2)/(2x + 3)) - 1) - 1))/(-3(-1cos(1\u03c0((-2x + 2)/(2x + 3)) - 1) - 1) - 2)) + 1)) + 3)/(-3((1((-1(-1cos(1\u03c0((-2x + 2)/(2x + 3)) - 1) - 1))/(-3(-1cos(1\u03c0((-2x + 2)/(2x + 3)) - 1) - 1) - 2)) + 3)/(3((-1(-1cos(1\u03c0((-2x + 2)/(2x + 3)) - 1) - 1))/(-3(-1cos(1\u03c0((-2x + 2)/(2x + 3)) - 1) - 1) - 2)) + 1)) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "19", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-1((2(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) + 3)/(-1(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) - 1))^2 - 3((2(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) + 3)/(-1(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) - 1)) - 1) + 1)/(3(-1((2(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) + 3)/(-1(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) - 1))^2 - 3((2(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) + 3)/(-1(-3cos(1\u03c0(1x^2 - 1) + 1) - 3) - 1)) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2e^(2(-3|(2|(-1((-2x + 3)/(3x + 3))^2 + 4((-2x + 3)/(3x + 3)) - 1) + 1| + 2) + 3| + 2)) have 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 number of x-intercepts of the function f(x) = -1|(-1cos(2\u03c0(-3|(-4(3x^2 - 3x + 1)^2 + 5(3x^2 - 3x + 1) - 4) - 2| - 2) - 1) + 1) + 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "845", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(2\u03c0(-2|(2(2|((-2x - 2)/(-1x))| - 3)^2 - 5(2|((-2x - 2)/(-1x))| - 3) + 2) - 3| - 3) + 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "236", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((3(2sin(3\u03c0((1(-5x + 4) - 3)/(3(-5x + 4) - 2)) - 3) + 1) - 1)/(2(2sin(3\u03c0((1(-5x + 4) - 3)/(3(-5x + 4) - 2)) - 3) + 1) - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3|(2|(-1cos(3\u03c0(-5x + 1) - 3) + 1) - 3| - 3)| - 3) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(3\u03c0(-2|((-2(-4(-2|x - 3| + 2)^2 + 1(-2|x - 3| + 2) + 3))/(3(-4(-2|x - 3| + 2)^2 + 1(-2|x - 3| + 2) + 3) + 1)) + 2| + 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-1sin(3\u03c0((-1(1(-2x + 3) - 5))/(3(1(-2x + 3) - 5) + 1)) + 3)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(3(-5(-2sin(1\u03c0(-4x^2 + 3x - 2) - 1) - 2)^2 + 1(-2sin(1\u03c0(-4x^2 + 3x - 2) - 1) - 2) + 3)^2 + 1) - 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "652", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(2cos(3\u03c0(-3((2(-1|x - 2| + 3) - 1)/(1(-1|x - 2| + 3) + 2)) + 3)) - 1) + 2)/(1(2cos(3\u03c0(-3((2(-1|x - 2| + 3) - 1)/(1(-1|x - 2| + 3) + 2)) + 3)) - 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "425", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(2(4(1(-3cos(2\u03c0x + 3) + 2)^2 - 1(-3cos(2\u03c0x + 3) + 2) - 4) + 1)^2 + 3(4(1(-3cos(2\u03c0x + 3) + 2)^2 - 1(-3cos(2\u03c0x + 3) + 2) - 4) + 1) + 4)^2 - 2(2(4(1(-3cos(2\u03c0x + 3) + 2)^2 - 1(-3cos(2\u03c0x + 3) + 2) - 4) + 1)^2 + 3(4(1(-3cos(2\u03c0x + 3) + 2)^2 - 1(-3cos(2\u03c0x + 3) + 2) - 4) + 1) + 4) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(3cos(3\u03c0(5(-2|(4x + 3) - 1| + 3)^2 - 2(-2|(4x + 3) - 1| + 3) + 3) - 1) + 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "817", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((-3(2|(2((-2x - 1)/(1x))^2 - 4((-2x - 1)/(1x)) - 5) + 3| - 3) - 1)/(2(2|(2((-2x - 1)/(1x))^2 - 4((-2x - 1)/(1x)) - 5) + 3| - 3) - 1)) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1sin(1\u03c0(5((2(-4(5x - 5) + 2) - 3)/(2(-4(5x - 5) + 2) + 1)) - 1)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((3(-2(-1e^(2((-1x - 3)/(2x + 3))) + 3)^2 + 5(-1e^(2((-1x - 3)/(2x + 3))) + 3) + 3) + 3)/(1(-2(-1e^(2((-1x - 3)/(2x + 3))) + 3)^2 + 5(-1e^(2((-1x - 3)/(2x + 3))) + 3) + 3))) - 2| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(3(-1|(-3|(2cos(3\u03c0x + 1))| - 3) + 2| + 1)^2 - 2(-1|(-3|(2cos(3\u03c0x + 1))| - 3) + 2| + 1) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-4(-3|(-1|((-2x - 1)/(2x + 3)) + 1| - 1) + 3| + 1)^2 + 3(-3|(-1|((-2x - 1)/(2x + 3)) + 1| - 1) + 3| + 1) + 5) + 3)/(2(-4(-3|(-1|((-2x - 1)/(2x + 3)) + 1| - 1) + 3| + 1)^2 + 3(-3|(-1|((-2x - 1)/(2x + 3)) + 1| - 1) + 3| + 1) + 5) - 1) have 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 number of x-intercepts of the function f(x) = (2(-3|(-3|(2sin(2\u03c0((-2x - 2)/(-3x + 1)))) - 2| + 1)| + 2))/(-2(-3|(-3|(2sin(2\u03c0((-2x - 2)/(-3x + 1)))) - 2| + 1)| + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(2\u03c0(4((1(2(1|x - 2| + 1)^2 - 1) - 3)/(-2(2(1|x - 2| + 1)^2 - 1) + 3))^2 - 2((1(2(1|x - 2| + 1)^2 - 1) - 3)/(-2(2(1|x - 2| + 1)^2 - 1) + 3)) - 2) + 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(3sin(3\u03c0(-5(-1|((-3x + 3)/(-1x + 3)) + 2|)^2 + 2(-1|((-3x + 3)/(-1x + 3)) + 2|) + 4) - 1) + 3) - 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "939", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-2|(1|(-4(3|x + 2| - 1)^2 - 3(3|x + 2| - 1) + 3)| - 2) - 2| + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2((-1(1(-1|(-2cos(3\u03c0x + 3) - 3) + 2|)^2 - 1(-1|(-2cos(3\u03c0x + 3) - 3) + 2|) - 3) - 1)/(3(1(-1|(-2cos(3\u03c0x + 3) - 3) + 2|)^2 - 1(-1|(-2cos(3\u03c0x + 3) - 3) + 2|) - 3) - 2))^2 + 3((-1(1(-1|(-2cos(3\u03c0x + 3) - 3) + 2|)^2 - 1(-1|(-2cos(3\u03c0x + 3) - 3) + 2|) - 3) - 1)/(3(1(-1|(-2cos(3\u03c0x + 3) - 3) + 2|)^2 - 1(-1|(-2cos(3\u03c0x + 3) - 3) + 2|) - 3) - 2)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(2(-1(-2cos(3\u03c0(3x + 3) - 3) - 2)^2 + 5(-2cos(3\u03c0(3x + 3) - 3) - 2) + 4) + 2) - 3| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "254", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1sin(1\u03c0(3(-2|(2|((2x - 3)/(3x - 2)) + 2| + 1)| + 3)^2 + 3(-2|(2|((2x - 3)/(3x - 2)) + 2| + 1)| + 3) + 3) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "221", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(3cos(3\u03c0(-1(2|(1|x - 1| - 3) - 2| + 1) + 3) - 1)) - 3)/(-1(3cos(3\u03c0(-1(2|(1|x - 1| - 3) - 2| + 1) + 3) - 1)) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(2((2((-1(-3cos(3\u03c0x - 1) - 1) + 1)/(1(-3cos(3\u03c0x - 1) - 1) - 2)) - 3)/(-1((-1(-3cos(3\u03c0x - 1) - 1) + 1)/(1(-3cos(3\u03c0x - 1) - 1) - 2)))) - 1) - 3)/(2(2((2((-1(-3cos(3\u03c0x - 1) - 1) + 1)/(1(-3cos(3\u03c0x - 1) - 1) - 2)) - 3)/(-1((-1(-3cos(3\u03c0x - 1) - 1) + 1)/(1(-3cos(3\u03c0x - 1) - 1) - 2)))) - 1) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-1sin(3\u03c0(-5(-1|(-1x) + 3| + 2)) - 3) + 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(2|(-5((1(2x^2 - 3x - 3) + 2)/(1(2x^2 - 3x - 3) + 3)) + 2) + 1| - 3) + 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(2(3(-4(2x^2 - 2) + 5)^2 - 5(-4(2x^2 - 2) + 5)) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(1\u03c0((3((-3((-3((-1x + 1)/(-3x - 2)) - 1)/(-1((-1x + 1)/(-3x - 2)) - 1)) + 3)/(-1((-3((-1x + 1)/(-3x - 2)) - 1)/(-1((-1x + 1)/(-3x - 2)) - 1)) - 1)) + 1)/(2((-3((-3((-1x + 1)/(-3x - 2)) - 1)/(-1((-1x + 1)/(-3x - 2)) - 1)) + 3)/(-1((-3((-1x + 1)/(-3x - 2)) - 1)/(-1((-1x + 1)/(-3x - 2)) - 1)) - 1)) - 1)) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "174", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-2(2(-2|(-1|x + 2| + 2) - 2| + 1)^2 + 5(-2|(-1|x + 2| + 2) - 2| + 1) + 2)^2 - 4(2(-2|(-1|x + 2| + 2) - 2| + 1)^2 + 5(-2|(-1|x + 2| + 2) - 2| + 1) + 2) + 2) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(3|(3((-2(2|x - 2| - 2) + 3)/(2(2|x - 2| - 2) + 3))) - 1|) - 1)/(2(3|(3((-2(2|x - 2| - 2) + 3)/(2(2|x - 2| - 2) + 3))) - 1|) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(2cos(3\u03c0((-2(-4(1x^2 + 4x - 3)^2 - 4(1x^2 + 4x - 3) + 1) - 1)/(-3(-4(1x^2 + 4x - 3)^2 - 4(1x^2 + 4x - 3) + 1))) + 1) + 1) + 1| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3(3(-3|((-3x + 1)/(-2x - 2)) - 3| + 1) - 3) - 5)^2 - 2(-3(3(-3|((-3x + 1)/(-2x - 2)) - 3| + 1) - 3) - 5) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-2(-2e^(1(2(5x + 1) - 4)) + 1)^2 + 2(-2e^(1(2(5x + 1) - 4)) + 1) + 4) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(1(-2(5(3sin(2\u03c0x - 1) - 1)^2 + 3(3sin(2\u03c0x - 1) - 1) - 1) + 5)^2 + 3(-2(5(3sin(2\u03c0x - 1) - 1)^2 + 3(3sin(2\u03c0x - 1) - 1) - 1) + 5) + 1)^2 - 4(1(-2(5(3sin(2\u03c0x - 1) - 1)^2 + 3(3sin(2\u03c0x - 1) - 1) - 1) + 5)^2 + 3(-2(5(3sin(2\u03c0x - 1) - 1)^2 + 3(3sin(2\u03c0x - 1) - 1) - 1) + 5) + 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(1\u03c0(3(-1|(-1|(-3|x + 2| + 2) - 2|) - 3| - 1)) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((1(2sin(3\u03c0(2|((-2x + 1)/(1x + 3)) + 3|) - 2)) + 2)/(-1(2sin(3\u03c0(2|((-2x + 1)/(1x + 3)) + 3|) - 2)) + 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "149", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-2(-1|(-3(-4x)) + 2| + 2) - 3) - 2| + 3 have 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 number of x-intercepts of the function f(x) = 2(3|(2|(-2|(5x - 1) + 1| - 1) + 3| + 2) - 2| - 1) + 1 where -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 number of x-intercepts of the function f(x) = -4(3(4(3|((-1x - 1)/(3x + 1)) - 1| - 3)^2 + 2(3|((-1x - 1)/(3x + 1)) - 1| - 3) - 4) + 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(3((1(-2(1x^2 + 2x + 3) + 5))/(2(-2(1x^2 + 2x + 3) + 5) + 3))^2 - 4((1(-2(1x^2 + 2x + 3) + 5))/(2(-2(1x^2 + 2x + 3) + 5) + 3)) + 1) - 3| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(3cos(1\u03c0(-2|(2(3|x - 2| + 3) + 2) - 2| + 2) - 1) + 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1e^(1(-1(-3(-2x - 4)^2 + 5(-2x - 4) + 1) - 3)) + 3)^2 - 1(-1e^(1(-1(-3(-2x - 4)^2 + 5(-2x - 4) + 1) - 3)) + 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-3(-3((-1(-2x^2 + 1x + 4))/(1(-2x^2 + 1x + 4) - 3))^2 + 5((-1(-2x^2 + 1x + 4))/(1(-2x^2 + 1x + 4) - 3)) - 3) - 5) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5((-3(-2(-4(3e^(2x) - 2)^2 - 5(3e^(2x) - 2))^2 - 5(-4(3e^(2x) - 2)^2 - 5(3e^(2x) - 2)) + 2) - 2)/(-2(-2(-4(3e^(2x) - 2)^2 - 5(3e^(2x) - 2))^2 - 5(-4(3e^(2x) - 2)^2 - 5(3e^(2x) - 2)) + 2)))^2 - 5((-3(-2(-4(3e^(2x) - 2)^2 - 5(3e^(2x) - 2))^2 - 5(-4(3e^(2x) - 2)^2 - 5(3e^(2x) - 2)) + 2) - 2)/(-2(-2(-4(3e^(2x) - 2)^2 - 5(3e^(2x) - 2))^2 - 5(-4(3e^(2x) - 2)^2 - 5(3e^(2x) - 2)) + 2))) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(2\u03c0(3(2(-5(2x - 5)^2 - 2)^2 - 4(-5(2x - 5)^2 - 2) + 5) + 1)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "289", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0((1(1(-4(3x)^2 + 3(3x) - 1) + 5) + 1)/(-2(1(-4(3x)^2 + 3(3x) - 1) + 5) + 3)) - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0((-2(1(-1(3x - 5) - 4) - 5) + 2)/(-2(1(-1(3x - 5) - 4) - 5))) - 2) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(2(-2sin(2\u03c0(4(-1|x - 1| + 3)^2 + 5(-1|x - 1| + 3) - 1) - 1) - 3)^2 + 1(-2sin(2\u03c0(4(-1|x - 1| + 3)^2 + 5(-1|x - 1| + 3) - 1) - 1) - 3) - 5) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "805", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3sin(2\u03c0(3(-5(4(-2|x - 3| - 2) + 3)^2 - 4(4(-2|x - 3| - 2) + 3) - 2)^2 + 2(-5(4(-2|x - 3| - 2) + 3)^2 - 4(4(-2|x - 3| - 2) + 3) - 2) - 4) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((2(-3(-3(-3x)^2 + 5(-3x))^2 - 5(-3(-3x)^2 + 5(-3x)) + 2) + 3)/(1(-3(-3(-3x)^2 + 5(-3x))^2 - 5(-3(-3x)^2 + 5(-3x)) + 2) + 2))^2 - 3((2(-3(-3(-3x)^2 + 5(-3x))^2 - 5(-3(-3x)^2 + 5(-3x)) + 2) + 3)/(1(-3(-3(-3x)^2 + 5(-3x))^2 - 5(-3(-3x)^2 + 5(-3x)) + 2) + 2)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(3|(-5(3(-5x + 3)^2 - 3(-5x + 3) - 1) - 2) - 2| - 1) - 2 where -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 number of x-intercepts of the function f(x) = (3(-2(2(-1(-3cos(3\u03c0x))^2 + 5) - 3) - 4))/(3(-2(2(-1(-3cos(3\u03c0x))^2 + 5) - 3) - 4) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(1(5(-3|(2|x - 1| + 2) + 3| + 2) - 5) - 5) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1800", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-1(3((2(-2cos(2\u03c0x + 1) + 3) - 2)/(-2(-2cos(2\u03c0x + 1) + 3) - 2))^2 - 5((2(-2cos(2\u03c0x + 1) + 3) - 2)/(-2(-2cos(2\u03c0x + 1) + 3) - 2)) - 5) - 2))/(-1(-1(3((2(-2cos(2\u03c0x + 1) + 3) - 2)/(-2(-2cos(2\u03c0x + 1) + 3) - 2))^2 - 5((2(-2cos(2\u03c0x + 1) + 3) - 2)/(-2(-2cos(2\u03c0x + 1) + 3) - 2)) - 5) - 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0((-2(1(1((2x + 2)/(-1x)) - 3) + 3))/(1(1(1((2x + 2)/(-1x)) - 3) + 3) + 3))) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "127", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(2\u03c0(4((1((-2(-1x - 1) - 3)/(1(-1x - 1) + 3)) - 2)/(-3((-2(-1x - 1) - 3)/(1(-1x - 1) + 3)) + 4))^2 + 2((1((-2(-1x - 1) - 3)/(1(-1x - 1) + 3)) - 2)/(-3((-2(-1x - 1) - 3)/(1(-1x - 1) + 3)) + 4))) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-2sin(1\u03c0(-5(3|(3|x - 2| + 2) - 1| + 3) + 3))) - 1| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "439", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(2cos(1\u03c0((2((1((-2x)/(-3x + 1)) + 3)/(2((-2x)/(-3x + 1)) + 2)) - 1)/(3((1((-2x)/(-3x + 1)) + 3)/(2((-2x)/(-3x + 1)) + 2)) + 2))))^2 + 5(2cos(1\u03c0((2((1((-2x)/(-3x + 1)) + 3)/(2((-2x)/(-3x + 1)) + 2)) - 1)/(3((1((-2x)/(-3x + 1)) + 3)/(2((-2x)/(-3x + 1)) + 2)) + 2)))) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(1|((2(4(2cos(1\u03c0x + 3) - 1) + 4) + 1)/(-1(4(2cos(1\u03c0x + 3) - 1) + 4) - 2)) - 1| - 1) - 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((-1(4(-1(1x - 2)^2 + 1(1x - 2) + 1)^2 - 1(-1(1x - 2)^2 + 1(1x - 2) + 1) - 1) + 2)/(-2(4(-1(1x - 2)^2 + 1(1x - 2) + 1)^2 - 1(-1(1x - 2)^2 + 1(1x - 2) + 1) - 1) + 1)) + 3 have 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 number of x-intercepts of the function f(x) = 3(-3sin(2\u03c0(1|((1(2|x + 1| - 1) + 3)/(-2(2|x + 1| - 1) + 3)) - 2| - 3) - 3) - 1) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "106", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((1(3|(-1(-3|x + 2| + 3))| - 3) - 3)/(-1(3|(-1(-3|x + 2| + 3))| - 3) + 2)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1((3(-2sin(1\u03c0(-5x + 5)) + 1) - 1)/(-3(-2sin(1\u03c0(-5x + 5)) + 1))) + 5) - 2)/(-3(1((3(-2sin(1\u03c0(-5x + 5)) + 1) - 1)/(-3(-2sin(1\u03c0(-5x + 5)) + 1))) + 5) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(-1(1(3(-2|x - 3| + 2) + 1)^2 - 5(3(-2|x - 3| + 2) + 1) - 2)^2 + 4(1(3(-2|x - 3| + 2) + 1)^2 - 5(3(-2|x - 3| + 2) + 1) - 2) + 3) - 1)/(3(-1(1(3(-2|x - 3| + 2) + 1)^2 - 5(3(-2|x - 3| + 2) + 1) - 2)^2 + 4(1(3(-2|x - 3| + 2) + 1)^2 - 5(3(-2|x - 3| + 2) + 1) - 2) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((-3(-1(2(-1|x - 3|) + 5)^2 - 5(2(-1|x - 3|) + 5) - 3) - 1)/(3(-1(2(-1|x - 3|) + 5)^2 - 5(2(-1|x - 3|) + 5) - 3))) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-2(-2cos(3\u03c0(4(-4x - 5) - 4) - 1) - 1) - 4) + 3)/(-1(-2(-2cos(3\u03c0(4(-4x - 5) - 4) - 1) - 1) - 4) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "960", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-3|(-1|(2cos(1\u03c0((-2x - 1)/(1x + 2)) + 3)) - 2| + 1) + 3| + 2) - 1| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(4(-1(-1sin(2\u03c0(2x + 5) - 3) + 3) + 1) + 4)^2 - 4(4(-1(-1sin(2\u03c0(2x + 5) - 3) + 3) + 1) + 4) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-2cos(2\u03c0(-2|(2|(5x + 5) + 2| + 2) - 1|) + 1) - 3) - 3)/(2(-2cos(2\u03c0(-2|(2|(5x + 5) + 2| + 2) - 1|) + 1) - 3) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "800", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1((-3(-1e^(2(3x - 2)) + 2) - 2)/(-1(-1e^(2(3x - 2)) + 2) - 2))^2 + 1((-3(-1e^(2(3x - 2)) + 2) - 2)/(-1(-1e^(2(3x - 2)) + 2) - 2)) - 1)^2 - 1(1((-3(-1e^(2(3x - 2)) + 2) - 2)/(-1(-1e^(2(3x - 2)) + 2) - 2))^2 + 1((-3(-1e^(2(3x - 2)) + 2) - 2)/(-1(-1e^(2(3x - 2)) + 2) - 2)) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(1\u03c0((3((-3((-1((2x + 2)/(-3x + 4)))/(-1((2x + 2)/(-3x + 4)) + 2)) - 2)/(-2((-1((2x + 2)/(-3x + 4)))/(-1((2x + 2)/(-3x + 4)) + 2)) - 1)) + 1)/(-1((-3((-1((2x + 2)/(-3x + 4)))/(-1((2x + 2)/(-3x + 4)) + 2)) - 2)/(-2((-1((2x + 2)/(-3x + 4)))/(-1((2x + 2)/(-3x + 4)) + 2)) - 1)) - 3)) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(2(1(1(1x^2 - 4x + 1)^2 + 3(1x^2 - 4x + 1) - 5)^2 - 3(1(1x^2 - 4x + 1)^2 + 3(1x^2 - 4x + 1) - 5) - 1)) - 1)/(-2(2(1(1(1x^2 - 4x + 1)^2 + 3(1x^2 - 4x + 1) - 5)^2 - 3(1(1x^2 - 4x + 1)^2 + 3(1x^2 - 4x + 1) - 5) - 1))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(1|((-3(-2sin(1\u03c0(1x^2 + 4x + 3) + 2) + 2))/(1(-2sin(1\u03c0(1x^2 + 4x + 3) + 2) + 2) - 2)) - 2|)^2 + 3(1|((-3(-2sin(1\u03c0(1x^2 + 4x + 3) + 2) + 2))/(1(-2sin(1\u03c0(1x^2 + 4x + 3) + 2) + 2) - 2)) - 2|) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "384", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0(-4(-1|(4(-5x + 2)^2 - 4) + 1| - 2) - 1) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1236", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-1|(4(-3sin(2\u03c0(2x^2 + 1) + 1) - 3)^2 + 1) - 2| + 3) - 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(3sin(2\u03c0(-2(4((-2x + 3)/(3x + 1))^2 + 5((-2x + 3)/(3x + 1)) + 4)) + 2)) + 2)/(3(3sin(2\u03c0(-2(4((-2x + 3)/(3x + 1))^2 + 5((-2x + 3)/(3x + 1)) + 4)) + 2)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(-1(-2((-2(4x + 1) + 3)/(3(4x + 1)))^2 - 4((-2(4x + 1) + 3)/(3(4x + 1))) - 4)^2 + 4(-2((-2(4x + 1) + 3)/(3(4x + 1)))^2 - 4((-2(4x + 1) + 3)/(3(4x + 1))) - 4) - 2) - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "73", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(3\u03c0(3(-2(5(4x - 1)^2 - 5(4x - 1) - 5)^2 + 3(5(4x - 1)^2 - 5(4x - 1) - 5) - 4) - 5)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "145", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-4(-5((-1(-1cos(1\u03c0x + 2) - 2) - 1)/(-2(-1cos(1\u03c0x + 2) - 2) - 3))^2 + 1((-1(-1cos(1\u03c0x + 2) - 2) - 1)/(-2(-1cos(1\u03c0x + 2) - 2) - 3))) - 5) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(2((1(1(-4x^2 - 2x) + 2) - 1)/(-2(1(-4x^2 - 2x) + 2) - 3))^2 - 3((1(1(-4x^2 - 2x) + 2) - 1)/(-2(1(-4x^2 - 2x) + 2) - 3)) + 5) + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(-3|(2(3(-1x - 2) + 2) + 5) + 2| + 3)^2 + 4(-3|(2(3(-1x - 2) + 2) + 5) + 2| + 3) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0(-4((3(-1|(2|x - 2| - 3) + 3| + 3) + 1)/(-1(-1|(2|x - 2| - 3) + 3| + 3))) - 4) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2|(4(-4((-1x + 3)/(-2x + 1))^2 + 2((-1x + 3)/(-2x + 1)) + 2) + 4) - 1| + 1) - 2)/(-1(2|(4(-4((-1x + 3)/(-2x + 1))^2 + 2((-1x + 3)/(-2x + 1)) + 2) + 4) - 1| + 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(2|(-2e^(2((2((3x)/(2x - 1)) + 3)/(-1((3x)/(2x - 1)) + 3))) - 1) + 2| - 1)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3|(3|(1|(-1|x - 3| - 1)| - 1) - 1| - 2) + 1|)^2 - 5(-3|(3|(1|(-1|x - 3| - 1)| - 1) - 1| - 2) + 1|) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0((-3(-1|(-2|(-2|x| + 1)| - 2) - 2| + 3) + 2)/(1(-1|(-2|(-2|x| + 1)| - 2) - 2| + 3) - 2))) + 3 have 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 number of x-intercepts of the function f(x) = 1|(-1sin(2\u03c0((2(-2(5x^2 + 4x - 1) + 5) + 1)/(1(-2(5x^2 + 4x - 1) + 5) + 1)) - 2)) - 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(2\u03c0(4(4(-1|(4x^2 + 1x - 1) - 3| - 1))) + 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1499", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(2|(-1(-5(2|x - 3| - 1) + 5)^2 - 5(-5(2|x - 3| - 1) + 5) - 1)| - 1) + 1| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(4((3(-3e^(-1(-4x^2 - 5x)) + 2) + 3)/(-2(-3e^(-1(-4x^2 - 5x)) + 2) + 1)) - 3)| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-2(-2sin(1\u03c0(-1(5x + 4)^2 + 2(5x + 4) + 4))) - 4)^2 + 4(-2(-2sin(1\u03c0(-1(5x + 4)^2 + 2(5x + 4) + 4))) - 4) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "697", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(3sin(1\u03c0(-4((1(-3x - 5) + 2)/(2(-3x - 5))) - 3) + 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(2sin(2\u03c0(-2|(1(-1|x + 1| - 2) + 3) - 2| + 2) - 2) + 1)^2 + 1(2sin(2\u03c0(-2|(1(-1|x + 1| - 2) + 3) - 2| + 2) - 2) + 1) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-4((-1(-1((-2x - 3)/(1x + 2))^2 + 4((-2x - 3)/(1x + 2)) + 1) - 1)/(-1(-1((-2x - 3)/(1x + 2))^2 + 4((-2x - 3)/(1x + 2)) + 1) - 2))^2 + 2((-1(-1((-2x - 3)/(1x + 2))^2 + 4((-2x - 3)/(1x + 2)) + 1) - 1)/(-1(-1((-2x - 3)/(1x + 2))^2 + 4((-2x - 3)/(1x + 2)) + 1) - 2))) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1((-3(-2e^(-2(-1(-1|x + 1| + 2) - 3))) + 2)/(2(-2e^(-2(-1(-1|x + 1| + 2) - 3))) + 1))^2 + 1((-3(-2e^(-2(-1(-1|x + 1| + 2) - 3))) + 2)/(2(-2e^(-2(-1(-1|x + 1| + 2) - 3))) + 1)) + 4 where -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 number of x-intercepts of the function f(x) = (2(4(-1(3(-1cos(2\u03c0x) + 2) - 2) + 2)^2 + 3(-1(3(-1cos(2\u03c0x) + 2) - 2) + 2) - 2) + 1)/(-2(4(-1(3(-1cos(2\u03c0x) + 2) - 2) + 2)^2 + 3(-1(3(-1cos(2\u03c0x) + 2) - 2) + 2) - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(3|(1((-3((1x + 1)/(2x + 1)) + 3)/(3((1x + 1)/(2x + 1)) + 2))^2 - 3((-3((1x + 1)/(2x + 1)) + 3)/(3((1x + 1)/(2x + 1)) + 2)) - 1)| + 1) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(2(5(2|(-3x - 5) + 3|)^2 - 3(2|(-3x - 5) + 3|) - 3) + 1) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3|(-1(3(-1x - 1) - 2)^2 - 2(3(-1x - 1) - 2) + 3)| - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0(-5((-2((-1(-3x^2 - 4x - 2) - 3)/(-1(-3x^2 - 4x - 2) + 3)) - 3)/(1((-1(-3x^2 - 4x - 2) - 3)/(-1(-3x^2 - 4x - 2) + 3)) + 1))^2 - 5) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "209", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|((-2(5(1(-2|x - 2| + 2) + 5) - 5) + 2)/(-1(5(1(-2|x - 2| + 2) + 5) - 5) - 3)) - 1| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3((-1(-3(-2(-4x^2 + 1)^2 - 1(-4x^2 + 1))^2 + 1(-2(-4x^2 + 1)^2 - 1(-4x^2 + 1)) - 2) + 3)/(3(-3(-2(-4x^2 + 1)^2 - 1(-4x^2 + 1))^2 + 1(-2(-4x^2 + 1)^2 - 1(-4x^2 + 1)) - 2) + 1)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(2|(2|((-1(3x^2 - 4x - 3))/(-1(3x^2 - 4x - 3) - 2))| + 1) - 2| + 3)^2 - 3(2|(2|((-1(3x^2 - 4x - 3))/(-1(3x^2 - 4x - 3) - 2))| + 1) - 2| + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(-3|((3(-5(1x)^2 + 1(1x) - 4) + 3)/(-1(-5(1x)^2 + 1(1x) - 4))) + 1| + 1) - 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0(3|(5(-1|(-1x - 3)| - 3)^2 + 2(-1|(-1x - 3)| - 3) - 2)| - 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1469", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0(-4((-1(-3((-2x)/(-2x + 3)) + 1) + 3)/(2(-3((-2x)/(-2x + 3)) + 1) - 1)) + 3) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(3(-3|(5(5x - 5)^2 + 4(5x - 5) - 2) + 2|)^2 + 3(-3|(5(5x - 5)^2 + 4(5x - 5) - 2) + 2|) - 5) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-2(-3|(2|(3x^2 - 1x + 3) - 2| - 2) - 1|) - 5) + 2| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-3(3|(-2|(2x - 4) - 2| + 3)| - 1) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(-2(5(-1(1x^2 - 1x - 5) - 2) - 5) + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1724", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-5(-3|((-1(-2cos(1\u03c0x + 1) - 1) + 3)/(-1(-2cos(1\u03c0x + 1) - 1) - 1)) + 1| + 3)^2 + 3(-3|((-1(-2cos(1\u03c0x + 1) - 1) + 3)/(-1(-2cos(1\u03c0x + 1) - 1) - 1)) + 1| + 3) + 5)^2 + 4(-5(-3|((-1(-2cos(1\u03c0x + 1) - 1) + 3)/(-1(-2cos(1\u03c0x + 1) - 1) - 1)) + 1| + 3)^2 + 3(-3|((-1(-2cos(1\u03c0x + 1) - 1) + 3)/(-1(-2cos(1\u03c0x + 1) - 1) - 1)) + 1| + 3) + 5) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "70", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-3(1((3(-1cos(2\u03c0x + 3) - 2) + 3)/(-2(-1cos(2\u03c0x + 3) - 2) - 3))^2 - 5) + 5) - 2)/(-2(-3(1((3(-1cos(2\u03c0x + 3) - 2) + 3)/(-2(-1cos(2\u03c0x + 3) - 2) - 3))^2 - 5) + 5) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "62", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0(-4(-2(3(-4x - 1)^2 - 2)^2 + 5(3(-4x - 1)^2 - 2) - 2) + 2) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(5(-5(4(-1|x - 3| + 3)^2 - 3(-1|x - 3| + 3) - 3)^2 - 3(4(-1|x - 3| + 3)^2 - 3(-1|x - 3| + 3) - 3) + 3)^2 + 3(-5(4(-1|x - 3| + 3)^2 - 3(-1|x - 3| + 3) - 3)^2 - 3(4(-1|x - 3| + 3)^2 - 3(-1|x - 3| + 3) - 3) + 3) - 4) - 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-4(-4((1((1x - 1)/(-1x)) + 2)/(-2((1x - 1)/(-1x)) + 1))^2 - 4((1((1x - 1)/(-1x)) + 2)/(-2((1x - 1)/(-1x)) + 1)) + 2) + 2)^2 - 5(-4(-4((1((1x - 1)/(-1x)) + 2)/(-2((1x - 1)/(-1x)) + 1))^2 - 4((1((1x - 1)/(-1x)) + 2)/(-2((1x - 1)/(-1x)) + 1)) + 2) + 2) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-3(-2(1|(-5x - 2) - 3| - 1)^2 + 4(1|(-5x - 2) - 3| - 1)) + 1) + 1)/(2(-3(-2(1|(-5x - 2) - 3| - 1)^2 + 4(1|(-5x - 2) - 3| - 1)) + 1) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(3(-4(5(1|x| - 3)^2 + 3(1|x| - 3) - 1)^2 + 5)) - 2)/(-1(3(-4(5(1|x| - 3)^2 + 3(1|x| - 3) - 1)^2 + 5)) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-1(-3cos(2\u03c0(-2|(-1|x - 1|)| + 3) + 3) + 1)^2 - 1(-3cos(2\u03c0(-2|(-1|x - 1|)| + 3) + 3) + 1) + 3) - 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5((-3(-2(1(-5x + 2)^2 - 5(-5x + 2) - 3) - 4) + 2)/(1(-2(1(-5x + 2)^2 - 5(-5x + 2) - 3) - 4) + 3))^2 + 2((-3(-2(1(-5x + 2)^2 - 5(-5x + 2) - 3) - 4) + 2)/(1(-2(1(-5x + 2)^2 - 5(-5x + 2) - 3) - 4) + 3)) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-3cos(1\u03c0(3|(-3|(-2|x + 2| - 1) - 2| + 1)| - 2) - 2) + 3)^2 - 5(-3cos(1\u03c0(3|(-3|(-2|x + 2| - 1) - 2| + 1)| - 2) - 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "520", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(-4(-1(1|(3x^2 + 5x + 3) + 1| - 1) + 1)^2 - 4) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "684", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(-3(-3sin(3\u03c0(-1((3x + 3)/(-1x + 3)) + 5))) - 4) + 1| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2((1(1(-3cos(1\u03c0(5x - 3) - 3) - 3) + 1) - 1)/(-2(1(-3cos(1\u03c0(5x - 3) - 3) - 3) + 1) - 2)) - 3)/(-2((1(1(-3cos(1\u03c0(5x - 3) - 3) - 3) + 1) - 1)/(-2(1(-3cos(1\u03c0(5x - 3) - 3) - 3) + 1) - 2)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "100", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((1(-3|(2|(2x + 3) + 3| - 2) + 1| + 1) - 1)/(3(-3|(2|(2x + 3) + 3| - 2) + 1| + 1) - 2)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(5(-3sin(1\u03c0((1(1x - 3) - 1)/(-1(1x - 3) + 3)) + 2)) + 4)^2 - 1(5(-3sin(1\u03c0((1(1x - 3) - 1)/(-1(1x - 3) + 3)) + 2)) + 4) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-2|(1|((2(1x^2 - 5x - 4) + 1)/(2(1x^2 - 5x - 4) + 2)) - 2| - 2) - 3| + 2) - 2)/(-2(-2|(1|((2(1x^2 - 5x - 4) + 1)/(2(1x^2 - 5x - 4) + 2)) - 2| - 2) - 3| + 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4((2((2(-4(4x^2 - 3x - 4)^2 + 3(4x^2 - 3x - 4)))/(-2(-4(4x^2 - 3x - 4)^2 + 3(4x^2 - 3x - 4)) - 2)) - 1)/(2((2(-4(4x^2 - 3x - 4)^2 + 3(4x^2 - 3x - 4)))/(-2(-4(4x^2 - 3x - 4)^2 + 3(4x^2 - 3x - 4)) - 2)) - 3)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(-4(1sin(2\u03c0(1|(-2|x + 2|) - 1| - 2) - 3) - 2)^2 - 2(1sin(2\u03c0(1|(-2|x + 2|) - 1| - 2) - 3) - 2) + 1) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-3(2cos(3\u03c0(-1(4x^2 - 4x + 3) - 3) + 2) - 1) + 2)/(1(2cos(3\u03c0(-1(4x^2 - 4x + 3) - 3) + 2) - 1)))^2 - 4((-3(2cos(3\u03c0(-1(4x^2 - 4x + 3) - 3) + 2) - 1) + 2)/(1(2cos(3\u03c0(-1(4x^2 - 4x + 3) - 3) + 2) - 1))) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "367", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-2(-2sin(1\u03c0(-4((-2x + 1)/(-3x + 1))^2 - 5)) - 1) + 3)| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-1(-2(-4(3sin(3\u03c0x + 1)) + 1) + 4)^2 + 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(3cos(1\u03c0(2((2(5x^2 - 5x + 3) + 1)/(-1(5x^2 - 5x + 3) - 3))^2) + 2) + 1) - 3)/(-1(3cos(1\u03c0(2((2(5x^2 - 5x + 3) + 1)/(-1(5x^2 - 5x + 3) - 3))^2) + 2) + 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(-2|((-1(1|(-4x - 3) + 3| - 1) + 1)/(-2(1|(-4x - 3) + 3| - 1) + 3))| + 3) - 1)/(-2(-2|((-1(1|(-4x - 3) + 3| - 1) + 1)/(-2(1|(-4x - 3) + 3| - 1) + 3))| + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3|(1(-3cos(2\u03c0(-2x + 2) - 2) - 3)^2 - 2(-3cos(2\u03c0(-2x + 2) - 2) - 3) + 4) - 3| + 1) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-3cos(1\u03c0((-1(-3|(-1x^2 + 5x + 5) + 1|) + 3)/(3(-3|(-1x^2 + 5x + 5) + 1|) - 1))) + 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(1((-2(1(-2cos(3\u03c0x - 2) - 2)^2 - 3(-2cos(3\u03c0x - 2) - 2) - 4) + 1)/(-1(1(-2cos(3\u03c0x - 2) - 2)^2 - 3(-2cos(3\u03c0x - 2) - 2) - 4) - 3))^2 - 4((-2(1(-2cos(3\u03c0x - 2) - 2)^2 - 3(-2cos(3\u03c0x - 2) - 2) - 4) + 1)/(-1(1(-2cos(3\u03c0x - 2) - 2)^2 - 3(-2cos(3\u03c0x - 2) - 2) - 4) - 3)) - 5) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-2(3(2cos(3\u03c0(5x - 3) - 2)) - 4) - 3) + 2| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(3(-1|(1(2sin(2\u03c0x) - 1) + 4) - 1| + 3) - 4) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(1sin(1\u03c0(-4(1|(2x^2 - 2x - 5) - 2|)^2 - 1(1|(2x^2 - 2x - 5) - 2|) - 2) - 2) + 1) + 1)/(-2(1sin(1\u03c0(-4(1|(2x^2 - 2x - 5) - 2|)^2 - 1(1|(2x^2 - 2x - 5) - 2|) - 2) - 2) + 1) - 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1276", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(1(-3|(-5(1|x| - 1) - 4) + 3| - 1) - 5) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "900", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(2|(-4(-5(-1x - 5)^2 - 4(-1x - 5) + 4)^2 + 5(-5(-1x - 5)^2 - 4(-1x - 5) + 4) + 5) + 1| - 1) - 2)/(3(2|(-4(-5(-1x - 5)^2 - 4(-1x - 5) + 4)^2 + 5(-5(-1x - 5)^2 - 4(-1x - 5) + 4) + 5) + 1| - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3((1((-2(3|x - 1| - 2) - 3)/(2(3|x - 1| - 2) - 3)) - 1)/(1((-2(3|x - 1| - 2) - 3)/(2(3|x - 1| - 2) - 3))))^2 + 4((1((-2(3|x - 1| - 2) - 3)/(2(3|x - 1| - 2) - 3)) - 1)/(1((-2(3|x - 1| - 2) - 3)/(2(3|x - 1| - 2) - 3)))) + 2) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(5(-1|((-3(1x^2 + 5x - 4) + 1)/(-1(1x^2 + 5x - 4) + 3)) + 3| + 3)^2 + 1(-1|((-3(1x^2 + 5x - 4) + 1)/(-1(1x^2 + 5x - 4) + 3)) + 3| + 3) - 3))/(1(5(-1|((-3(1x^2 + 5x - 4) + 1)/(-1(1x^2 + 5x - 4) + 3)) + 3| + 3)^2 + 1(-1|((-3(1x^2 + 5x - 4) + 1)/(-1(1x^2 + 5x - 4) + 3)) + 3| + 3) - 3) + 2) have 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 number of x-intercepts of the function f(x) = 2cos(3\u03c0(1(-5(3|(5x^2 - 2) - 2| + 3) + 4)^2 + 5(-5(3|(5x^2 - 2) - 2| + 3) + 4) + 3) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "212", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3((-1((-3(-5(-2x^2 + 5x - 2) - 4))/(-1(-5(-2x^2 + 5x - 2) - 4) - 2)) + 3)/(2((-3(-5(-2x^2 + 5x - 2) - 4))/(-1(-5(-2x^2 + 5x - 2) - 4) - 2)) - 3))^2 - 1((-1((-3(-5(-2x^2 + 5x - 2) - 4))/(-1(-5(-2x^2 + 5x - 2) - 4) - 2)) + 3)/(2((-3(-5(-2x^2 + 5x - 2) - 4))/(-1(-5(-2x^2 + 5x - 2) - 4) - 2)) - 3)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0(-4(1(-5(5x + 2)^2 + 5(5x + 2) + 5)^2 - 2(-5(5x + 2)^2 + 5(5x + 2) + 5) - 2) - 4) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "296", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(1cos(3\u03c0(-1(3(4x^2 + 4x + 1) - 1))) + 2) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1288", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-3|(-3(3|(-1|x - 2| + 1)| - 1)^2 + 1) + 1| + 1) - 1| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((-3((3(3|(3sin(2\u03c0x + 2) + 1) - 2| - 2) + 1)/(1(3|(3sin(2\u03c0x + 2) + 1) - 2| - 2) + 1)) + 2)/(3((3(3|(3sin(2\u03c0x + 2) + 1) - 2| - 2) + 1)/(1(3|(3sin(2\u03c0x + 2) + 1) - 2| - 2) + 1)) - 1)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(3sin(3\u03c0(1(-2(3|x| - 1) - 3) + 4) - 2) + 3)^2 + 4(3sin(3\u03c0(1(-2(3|x| - 1) - 3) + 4) - 2) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3|(-2((-3(-3cos(1\u03c0x + 2) - 2) + 3)/(-2(-3cos(1\u03c0x + 2) - 2) + 3)) + 4) - 2| - 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-1e^(-2(-1(-3|((-1x - 3)/(2x + 1)) + 2| - 3) - 5)) + 2)| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0(2|(1(4(-1|x + 1| + 3) + 1)^2 - 5(4(-1|x + 1| + 3) + 1) - 3) + 1| + 3) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1513", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-4(2|(-1(3|x + 3| - 1)^2 - 4(3|x + 3| - 1)) + 2| - 3) + 4) + 1)/(3(-4(2|(-1(3|x + 3| - 1)^2 - 4(3|x + 3| - 1)) + 2| - 3) + 4) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-1|(-1(-1((2x + 2)/(1x))^2 - 1((2x + 2)/(1x)) - 1) - 4) + 1| + 2) + 1)/(-1(-1|(-1(-1((2x + 2)/(1x))^2 - 1((2x + 2)/(1x)) - 1) - 4) + 1| + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-2cos(1\u03c0((-1(-1(-2|x - 2| + 3) - 5))/(-3(-1(-2|x - 2| + 3) - 5) - 2)) + 3)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(3|(-1|((-1((3x - 3)/(1x + 1)))/(-1((3x - 3)/(1x + 1)) - 1)) - 1| + 1) + 3| + 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "21", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2((2(-5(2cos(2\u03c0(1x + 5) - 2) + 2)^2 + 3(2cos(2\u03c0(1x + 5) - 2) + 2) + 2) + 1)/(-3(-5(2cos(2\u03c0(1x + 5) - 2) + 2)^2 + 3(2cos(2\u03c0(1x + 5) - 2) + 2) + 2) + 4)) - 2)/(-1((2(-5(2cos(2\u03c0(1x + 5) - 2) + 2)^2 + 3(2cos(2\u03c0(1x + 5) - 2) + 2) + 2) + 1)/(-3(-5(2cos(2\u03c0(1x + 5) - 2) + 2)^2 + 3(2cos(2\u03c0(1x + 5) - 2) + 2) + 2) + 4)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(3\u03c0(-4(2(-1|(-5x^2 - 1x - 4) - 3| - 1)^2 + 3(-1|(-5x^2 - 1x - 4) - 3| - 1) + 5) - 2)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "566", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1((3(-1|(-1((2x - 2)/(3x - 2))^2 - 2((2x - 2)/(3x - 2)) - 1) + 3| + 2))/(2(-1|(-1((2x - 2)/(3x - 2))^2 - 2((2x - 2)/(3x - 2)) - 1) + 3| + 2) - 3)) + 3)/(-3((3(-1|(-1((2x - 2)/(3x - 2))^2 - 2((2x - 2)/(3x - 2)) - 1) + 3| + 2))/(2(-1|(-1((2x - 2)/(3x - 2))^2 - 2((2x - 2)/(3x - 2)) - 1) + 3| + 2) - 3))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(4(-2cos(3\u03c0(-4(2x + 3)^2 + 5(2x + 3) + 1) - 2) - 3)^2 + 5(-2cos(3\u03c0(-4(2x + 3)^2 + 5(2x + 3) + 1) - 2) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1097", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(4(2(-3|(-3|x| + 1) + 2|)^2 - 5(-3|(-3|x| + 1) + 2|)) - 5) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(1(-2|((1(2|x + 2| - 3) + 1)/(-1(2|x + 2| - 3))) - 1| + 1)^2 + 5(-2|((1(2|x + 2| - 3) + 1)/(-1(2|x + 2| - 3))) - 1| + 1) - 5)^2 + 2(1(-2|((1(2|x + 2| - 3) + 1)/(-1(2|x + 2| - 3))) - 1| + 1)^2 + 5(-2|((1(2|x + 2| - 3) + 1)/(-1(2|x + 2| - 3))) - 1| + 1) - 5) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2((1(3sin(3\u03c0(2|(3x^2 + 3x - 1)|) + 1) + 1) - 2)/(-1(3sin(3\u03c0(2|(3x^2 + 3x - 1)|) + 1) + 1) + 3))^2 + 2((1(3sin(3\u03c0(2|(3x^2 + 3x - 1)|) + 1) + 1) - 2)/(-1(3sin(3\u03c0(2|(3x^2 + 3x - 1)|) + 1) + 1) + 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "334", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((2(2sin(1\u03c0((-1((-1x + 2)/(1x + 2)) + 1)/(-2((-1x + 2)/(1x + 2)) - 1)) - 1) + 1))/(1(2sin(1\u03c0((-1((-1x + 2)/(1x + 2)) + 1)/(-2((-1x + 2)/(1x + 2)) - 1)) - 1) + 1) + 2))^2 - 3((2(2sin(1\u03c0((-1((-1x + 2)/(1x + 2)) + 1)/(-2((-1x + 2)/(1x + 2)) - 1)) - 1) + 1))/(1(2sin(1\u03c0((-1((-1x + 2)/(1x + 2)) + 1)/(-2((-1x + 2)/(1x + 2)) - 1)) - 1) + 1) + 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "102", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(1|((-2(-2cos(3\u03c0((1x - 2)/(-3x)) + 1) + 2) - 1)/(2(-2cos(3\u03c0((1x - 2)/(-3x)) + 1) + 2) - 1)) - 2|) - 3| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "64", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2((1(-3|(-1(-3|x - 2| + 2)) - 2| + 2) + 1)/(-3(-3|(-1(-3|x - 2| + 2)) - 2| + 2))) + 3)/(-2((1(-3|(-1(-3|x - 2| + 2)) - 2| + 2) + 1)/(-3(-3|(-1(-3|x - 2| + 2)) - 2| + 2))) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(4(2|(-2|(-2x + 5) + 3| + 1) + 2| - 3)^2 - 3(2|(-2|(-2x + 5) + 3| + 1) + 2| - 3) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(1e^(-2(-1|(-1(-3|x - 3| + 1) - 4) - 2|)) - 3)^2 + 1(1e^(-2(-1|(-1(-3|x - 3| + 1) - 4) - 2|)) - 3) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(3(-1|((-2(-3x - 2) - 3)/(-3(-3x - 2))) + 3| + 1)^2 + 3(-1|((-2(-3x - 2) - 3)/(-3(-3x - 2))) + 3| + 1) + 4) + 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "57", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(2(3sin(1\u03c0(-1((2x + 3)/(-1x - 3)) - 1) + 2) + 2) - 4) + 1)/(1(2(3sin(1\u03c0(-1((2x + 3)/(-1x - 3)) - 1) + 2) + 2) - 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(3(-3|(-3cos(2\u03c0((3x + 3)/(-1x - 2))) - 2) - 2| + 2)^2 - 2(-3|(-3cos(2\u03c0((3x + 3)/(-1x - 2))) - 2) - 2| + 2) - 5)^2 + 3(3(-3|(-3cos(2\u03c0((3x + 3)/(-1x - 2))) - 2) - 2| + 2)^2 - 2(-3|(-3cos(2\u03c0((3x + 3)/(-1x - 2))) - 2) - 2| + 2) - 5) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "46", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(2\u03c0((2(1((1((-3x)/(-1x - 2)) + 3)/(1((-3x)/(-1x - 2))))^2 + 3((1((-3x)/(-1x - 2)) + 3)/(1((-3x)/(-1x - 2)))) - 4) + 2)/(2(1((1((-3x)/(-1x - 2)) + 3)/(1((-3x)/(-1x - 2))))^2 + 3((1((-3x)/(-1x - 2)) + 3)/(1((-3x)/(-1x - 2)))) - 4))) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3cos(1\u03c0(2((1(1(-3x - 2) - 2) + 2)/(2(1(-3x - 2) - 2) - 1))^2 - 2((1(1(-3x - 2) - 2) + 2)/(2(1(-3x - 2) - 2) - 1)) + 3) - 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "28", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-1(2cos(1\u03c0(1((-3x - 2)/(2x - 3)) - 5) - 2) + 1)^2 - 4(2cos(1\u03c0(1((-3x - 2)/(2x - 3)) - 5) - 2) + 1) + 2) - 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "11", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-1(-4(2sin(2\u03c0(-1|x| + 2) + 1) + 1) - 5)^2 - 2(-4(2sin(2\u03c0(-1|x| + 2) + 1) + 1) - 5) + 4))/(-2(-1(-4(2sin(2\u03c0(-1|x| + 2) + 1) + 1) - 5)^2 - 2(-4(2sin(2\u03c0(-1|x| + 2) + 1) + 1) - 5) + 4) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-1(3(-4(-1x + 1)^2 + 3(-1x + 1) + 5)^2 - 2(-4(-1x + 1)^2 + 3(-1x + 1) + 5) + 2)^2 - 1(3(-4(-1x + 1)^2 + 3(-1x + 1) + 5)^2 - 2(-4(-1x + 1)^2 + 3(-1x + 1) + 5) + 2) + 3) + 2| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1cos(1\u03c0((1((-3(-3((2x)/(-2x + 3))^2 + 4((2x)/(-2x + 3)) - 1) - 2)/(3(-3((2x)/(-2x + 3))^2 + 4((2x)/(-2x + 3)) - 1) + 3)) + 3)/(2((-3(-3((2x)/(-2x + 3))^2 + 4((2x)/(-2x + 3)) - 1) - 2)/(3(-3((2x)/(-2x + 3))^2 + 4((2x)/(-2x + 3)) - 1) + 3)) - 3))) - 1 have 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 number of x-intercepts of the function f(x) = -1(3((2(-1(1x^2 - 5x - 3)^2 - 1(1x^2 - 5x - 3)) + 2)/(1(-1(1x^2 - 5x - 3)^2 - 1(1x^2 - 5x - 3)) - 3)) - 4) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4((-2(2(-1|(2sin(1\u03c0x - 2) - 3)| - 1)^2 + 3(-1|(2sin(1\u03c0x - 2) - 3)| - 1) - 2) + 2)/(2(2(-1|(2sin(1\u03c0x - 2) - 3)| - 1)^2 + 3(-1|(2sin(1\u03c0x - 2) - 3)| - 1) - 2) - 1))^2 - 5((-2(2(-1|(2sin(1\u03c0x - 2) - 3)| - 1)^2 + 3(-1|(2sin(1\u03c0x - 2) - 3)| - 1) - 2) + 2)/(2(2(-1|(2sin(1\u03c0x - 2) - 3)| - 1)^2 + 3(-1|(2sin(1\u03c0x - 2) - 3)| - 1) - 2) - 1)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(1|(3(1|(-4x^2 - 3x + 3) + 2| - 1) - 3) + 3| - 3)^2 + 4(1|(3(1|(-4x^2 - 3x + 3) + 2| - 1) - 3) + 3| - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(2cos(2\u03c0(-1(3|((2x)/(3x - 1)) + 3| - 2)^2 - 5(3|((2x)/(3x - 1)) + 3| - 2) + 2) + 1) - 3) + 3)/(2(2cos(2\u03c0(-1(3|((2x)/(3x - 1)) + 3| - 2)^2 - 5(3|((2x)/(3x - 1)) + 3| - 2) + 2) + 1) - 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "200", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(1(1(-2sin(2\u03c0(-3x + 4) - 2) - 3)^2)^2 - 3(1(-2sin(2\u03c0(-3x + 4) - 2) - 3)^2) + 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-4(3|((1(3x^2 - 2x - 2) - 2)/(1(3x^2 - 2x - 2) + 1)) + 1| - 2)^2 - 5(3|((1(3x^2 - 2x - 2) - 2)/(1(3x^2 - 2x - 2) + 1)) + 1| - 2) + 4) + 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(3\u03c0((3(2(2|(1x + 5) - 2| - 3)^2 - 1(2|(1x + 5) - 2| - 3)))/(-2(2(2|(1x + 5) - 2| - 3)^2 - 1(2|(1x + 5) - 2| - 3)) + 3)) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(-5(3(-1((-1x)/(-1x - 3)) - 4)^2 - 4(-1((-1x)/(-1x - 3)) - 4) - 5)^2 + 2(3(-1((-1x)/(-1x - 3)) - 4)^2 - 4(-1((-1x)/(-1x - 3)) - 4) - 5) - 3) - 3) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1210", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(3sin(3\u03c0((-1((-1(-3x^2 + 1x + 2) - 1)/(-1(-3x^2 + 1x + 2))) - 2)/(3((-1(-3x^2 + 1x + 2) - 1)/(-1(-3x^2 + 1x + 2))) + 2))) + 3) - 3| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(1(4((3(2cos(3\u03c0x) + 3) - 2)/(2(2cos(3\u03c0x) + 3) + 3))^2 - 4) + 5) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "31", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(2(-1(2e^(-2(-4x^2 - 1x + 5)) + 1) + 5)^2 + 5(-1(2e^(-2(-4x^2 - 1x + 5)) + 1) + 5) - 4) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(2sin(3\u03c0(-4((1((2x - 2)/(-1x + 2)))/(-3((2x - 2)/(-1x + 2)) + 2))) + 1) + 2) - 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-2sin(2\u03c0(4(-1|(5x^2 + 3x - 2) + 2| - 1)^2 - 2(-1|(5x^2 + 3x - 2) + 2| - 1) + 1)) + 1) + 2)/(1(-2sin(2\u03c0(4(-1|(5x^2 + 3x - 2) + 2| - 1)^2 - 2(-1|(5x^2 + 3x - 2) + 2| - 1) + 1)) + 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "173", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(2|(-3|(-1(1|x + 2| + 2)^2 + 3(1|x + 2| + 2) + 2) - 1| + 2) + 2| + 1)^2 + 1(2|(-3|(-1(1|x + 2| + 2)^2 + 3(1|x + 2| + 2) + 2) - 1| + 2) + 2| + 1) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-1cos(2\u03c0(2|(-2|((2x - 2)/(-1x + 3)) + 1| - 3) - 2| + 3)) - 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "121", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0((3(-4(2|(-2x + 4) - 2| + 2)^2 + 5(2|(-2x + 4) - 2| + 2) - 3) + 1)/(1(-4(2|(-2x + 4) - 2| + 2)^2 + 5(2|(-2x + 4) - 2| + 2) - 3) + 3)) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(1(-1|((1(-3e^(-1x) + 2) - 2)/(2(-3e^(-1x) + 2) - 1)) + 2| + 3)^2 + 5(-1|((1(-3e^(-1x) + 2) - 2)/(2(-3e^(-1x) + 2) - 1)) + 2| + 3)) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-1e^(-1(3|(3((-2x)/(1x - 2)) + 1) - 1| + 2)) - 3) + 2| - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(-1sin(2\u03c0(2|(2|(-2|x + 2| + 3) - 1|) + 2| - 3) - 3) - 1) + 2)/(-3(-1sin(2\u03c0(2|(2|(-2|x + 2| + 3) - 1|) + 2| - 3) - 3) - 1) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "318", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1(3(3|(1x) - 2|)^2 - 5(3|(1x) - 2|) + 3)^2 + 1(3(3|(1x) - 2|)^2 - 5(3|(1x) - 2|) + 3) + 4) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((-1(3(-2(2x + 1)^2 - 5(2x + 1) + 5)^2 - 2(-2(2x + 1)^2 - 5(2x + 1) + 5)) + 2)/(1(3(-2(2x + 1)^2 - 5(2x + 1) + 5)^2 - 2(-2(2x + 1)^2 - 5(2x + 1) + 5)) + 1)) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(1((2(-1|(-2cos(1\u03c0x + 3) + 3) - 1| + 3) - 1)/(1(-1|(-2cos(1\u03c0x + 3) + 3) - 1| + 3) + 2))^2 - 3((2(-1|(-2cos(1\u03c0x + 3) + 3) - 1| + 3) - 1)/(1(-1|(-2cos(1\u03c0x + 3) + 3) - 1| + 3) + 2))) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0(3|(1(5(-1|x + 3| - 2)^2 + 3(-1|x + 3| - 2) - 1) + 3)|) - 1) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1246", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2cos(3\u03c0(-3|(-2(2x + 3)^2 + 2(2x + 3) - 2) - 3| + 1) - 2) - 1) - 1)/(-3(2cos(3\u03c0(-3|(-2(2x + 3)^2 + 2(2x + 3) - 2) - 3| + 1) - 2) - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1435", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(1\u03c0(2|(1(-2|((3x - 1)/(-1x - 2)) + 1| + 2)^2 - 5(-2|((3x - 1)/(-1x - 2)) + 1| + 2) - 3) - 2|) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "485", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-4(-2sin(3\u03c0(-5(-1|x + 2| - 3) + 1) - 3) + 1)^2 - 5(-2sin(3\u03c0(-5(-1|x + 2| - 3) + 1) - 3) + 1) + 1) + 1)/(-2(-4(-2sin(3\u03c0(-5(-1|x + 2| - 3) + 1) - 3) + 1)^2 - 5(-2sin(3\u03c0(-5(-1|x + 2| - 3) + 1) - 3) + 1) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "300", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(3\u03c0(5(1((3((2x - 2)/(-1x - 2)) - 2)/(1((2x - 2)/(-1x - 2)))) - 4)^2 + 2(1((3((2x - 2)/(-1x - 2)) - 2)/(1((2x - 2)/(-1x - 2)))) - 4) + 1) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(2sin(3\u03c0((-1(1(1x^2 - 2x - 2)^2 - 5(1x^2 - 2x - 2) - 3) - 3)/(2(1(1x^2 - 2x - 2)^2 - 5(1x^2 - 2x - 2) - 3) - 1)) - 2)))/(2(2sin(3\u03c0((-1(1(1x^2 - 2x - 2)^2 - 5(1x^2 - 2x - 2) - 3) - 3)/(2(1(1x^2 - 2x - 2)^2 - 5(1x^2 - 2x - 2) - 3) - 1)) - 2)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-1e^(-2(1(2|(-5x + 4) - 2| - 1)^2 + 4)) + 1) - 2)/(-1(-1e^(-2(1(2|(-5x + 4) - 2| - 1)^2 + 4)) + 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(5(3((2(-5x + 1) - 1)/(-1(-5x + 1) - 2)) + 1)^2 - 2(3((2(-5x + 1) - 1)/(-1(-5x + 1) - 2)) + 1) - 5)^2 + 5(5(3((2(-5x + 1) - 1)/(-1(-5x + 1) - 2)) + 1)^2 - 2(3((2(-5x + 1) - 1)/(-1(-5x + 1) - 2)) + 1) - 5) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(5(-3|(-3e^(-2(-1x^2 - 2x + 1)) + 2) - 1| + 2) + 4) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(3\u03c0(-4(3|(4(2x^2 + 1x - 4) - 4) - 2| + 1) - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1582", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(1|(5(3cos(2\u03c0(-4x) - 1) + 2)^2 - 3(3cos(2\u03c0(-4x) - 1) + 2) - 3) + 1| - 3) + 1)/(-2(1|(5(3cos(2\u03c0(-4x) - 1) + 2)^2 - 3(3cos(2\u03c0(-4x) - 1) + 2) - 3) + 1| - 3) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "259", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3sin(2\u03c0(3|(1((1x + 1)/(2x + 3))^2 + 2((1x + 1)/(2x + 3))) + 2| + 3) - 3) - 1) - 1)/(2(3sin(2\u03c0(3|(1((1x + 1)/(2x + 3))^2 + 2((1x + 1)/(2x + 3))) + 2| + 3) - 3) - 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(-3|(-5(1|((2x + 2)/(-3x + 4)) - 1|) - 4)|) + 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "233", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-3(-5(-1(-4x^2 + 4x + 1)^2 - 5(-4x^2 + 4x + 1) - 5) + 4)^2 + 1) + 1)/(3(-3(-5(-1(-4x^2 + 4x + 1)^2 - 5(-4x^2 + 4x + 1) - 5) + 4)^2 + 1) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(3cos(3\u03c0(-3(-3(-1x^2 + 5x - 5)^2 + 3(-1x^2 + 5x - 5) + 5)^2 + 1(-3(-1x^2 + 5x - 5)^2 + 3(-1x^2 + 5x - 5) + 5)) + 3)) + 2| + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "579", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1((1(-1cos(3\u03c0(-1(2|x - 3| + 3) + 5) - 1) + 1) - 3)/(-3(-1cos(3\u03c0(-1(2|x - 3| + 3) + 5) - 1) + 1) + 2)) + 3)/(-2((1(-1cos(3\u03c0(-1(2|x - 3| + 3) + 5) - 1) + 1) - 3)/(-3(-1cos(3\u03c0(-1(2|x - 3| + 3) + 5) - 1) + 1) + 2)) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(-2(-3cos(3\u03c0(1(1|x - 1| + 2))) + 1) - 3) + 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-1(1|(5(1|x - 3| - 1)^2 + 3(1|x - 3| - 1) + 1) - 2| - 3)^2 - 2(1|(5(1|x - 3| - 1)^2 + 3(1|x - 3| - 1) + 1) - 2| - 3) + 4) + 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4((3(2((2(1|x + 1| - 2) - 3)/(1(1|x + 1| - 2) + 1))^2 + 3((2(1|x + 1| - 2) - 3)/(1(1|x + 1| - 2) + 1)) - 4) - 2)/(-1(2((2(1|x + 1| - 2) - 3)/(1(1|x + 1| - 2) + 1))^2 + 3((2(1|x + 1| - 2) - 3)/(1(1|x + 1| - 2) + 1)) - 4) - 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3|(-1|(-3sin(2\u03c0(5((3x - 3)/(1x - 2)) - 3) - 2) + 1) + 3|)| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "114", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(3\u03c0(-1|(4(-3|(-1x - 4) - 3| - 1) - 4) - 2|) + 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "720", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2((-2((-1(-3(4x^2)^2 + 4(4x^2) + 1) - 2)/(2(-3(4x^2)^2 + 4(4x^2) + 1) - 1)) - 2)/(-3((-1(-3(4x^2)^2 + 4(4x^2) + 1) - 2)/(2(-3(4x^2)^2 + 4(4x^2) + 1) - 1))))^2 - 3((-2((-1(-3(4x^2)^2 + 4(4x^2) + 1) - 2)/(2(-3(4x^2)^2 + 4(4x^2) + 1) - 1)) - 2)/(-3((-1(-3(4x^2)^2 + 4(4x^2) + 1) - 2)/(2(-3(4x^2)^2 + 4(4x^2) + 1) - 1)))) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(1sin(2\u03c0(-4((-3((3x - 3)/(-2x - 3)) - 3)/(-3((3x - 3)/(-2x - 3)) - 2)) - 1) - 2) - 3) + 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "79", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2((-3(-3cos(3\u03c0(2x + 2) - 2)) + 2)/(-1(-3cos(3\u03c0(2x + 2) - 2)) + 2)) + 1) + 2)/(2(2((-3(-3cos(3\u03c0(2x + 2) - 2)) + 2)/(-1(-3cos(3\u03c0(2x + 2) - 2)) + 2)) + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "68", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(1(-1|((-3((-3x - 3)/(-2x - 1)) + 3)/(2((-3x - 3)/(-2x - 1)) + 3)) - 1| + 1)^2 + 2(-1|((-3((-3x - 3)/(-2x - 1)) + 3)/(2((-3x - 3)/(-2x - 1)) + 3)) - 1| + 1) - 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0(4((-2(4((-1x + 2)/(-1x))^2 + 2((-1x + 2)/(-1x)) - 5) - 3)/(1(4((-1x + 2)/(-1x))^2 + 2((-1x + 2)/(-1x)) - 5) + 1))) - 3) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3((-1(-2|(1(-2x^2 + 2x - 4) + 3) + 2|) - 2)/(-2(-2|(1(-2x^2 + 2x - 4) + 3) + 2|))) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-1|(5((-1(-3cos(1\u03c0x + 3) - 1) + 2)/(3(-3cos(1\u03c0x + 3) - 1) + 3))) - 2|) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1cos(3\u03c0((-2(2|((2(-3x - 4) + 1)/(-1(-3x - 4))) - 3| + 1) + 3)/(-2(2|((2(-3x - 4) + 1)/(-1(-3x - 4))) - 3| + 1) - 3)) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(1cos(2\u03c0(-1(3((2x - 2)/(-2x - 2)) + 2) + 4) + 1) + 1) - 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-3|((-1((2(-1x^2 - 3x - 2) - 1)/(-3(-1x^2 - 3x - 2) - 1)) + 3)/(1((2(-1x^2 - 3x - 2) - 1)/(-3(-1x^2 - 3x - 2) - 1)) + 3))| + 2) + 2)/(-2(-3|((-1((2(-1x^2 - 3x - 2) - 1)/(-3(-1x^2 - 3x - 2) - 1)) + 3)/(1((2(-1x^2 - 3x - 2) - 1)/(-3(-1x^2 - 3x - 2) - 1)) + 3))| + 2) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3(5(-1(3cos(3\u03c0(-2x^2 + 1x + 4) - 2) - 2) - 5)^2 + 2(-1(3cos(3\u03c0(-2x^2 + 1x + 4) - 2) - 2) - 5) - 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1018", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3(3sin(3\u03c0(-4(-1|(-2x - 3) + 3| + 3)^2 + 1(-1|(-2x - 3) + 3| + 3) + 4) - 2) + 3)^2 + 4(3sin(3\u03c0(-4(-1|(-2x - 3) + 3| + 3)^2 + 1(-1|(-2x - 3) + 3| + 3) + 4) - 2) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1411", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4((2(2|((-2(2sin(1\u03c0x + 3) - 1))/(2(2sin(1\u03c0x + 3) - 1) - 3)) + 1| - 2) - 1)/(-2(2|((-2(2sin(1\u03c0x + 3) - 1))/(2(2sin(1\u03c0x + 3) - 1) - 3)) + 1| - 2) - 1)) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(3cos(1\u03c0(-3(-1(2x - 1) - 3)^2 - 3(-1(2x - 1) - 3) - 4) + 2) - 1) + 2)/(-3(3cos(1\u03c0(-3(-1(2x - 1) - 3)^2 - 3(-1(2x - 1) - 3) - 4) + 2) - 1) + 4) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "333", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(5(-1(-1(2x^2 - 4x - 5)^2 - 2)^2 - 2(-1(2x^2 - 4x - 5)^2 - 2))^2 + 1(-1(-1(2x^2 - 4x - 5)^2 - 2)^2 - 2(-1(2x^2 - 4x - 5)^2 - 2)) - 2) + 2)/(-1(5(-1(-1(2x^2 - 4x - 5)^2 - 2)^2 - 2(-1(2x^2 - 4x - 5)^2 - 2))^2 + 1(-1(-1(2x^2 - 4x - 5)^2 - 2)^2 - 2(-1(2x^2 - 4x - 5)^2 - 2)) - 2) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2e^(1(-5(1|(1|(-3x^2 - 2x + 3) + 2|) - 2|) + 5)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(4((-1(1sin(3\u03c0(-5x^2 - 2x - 4) - 3) - 1) - 3)/(1(1sin(3\u03c0(-5x^2 - 2x - 4) - 3) - 1) - 3))^2 + 5((-1(1sin(3\u03c0(-5x^2 - 2x - 4) - 3) - 1) - 3)/(1(1sin(3\u03c0(-5x^2 - 2x - 4) - 3) - 1) - 3)) - 5) - 2)/(1(4((-1(1sin(3\u03c0(-5x^2 - 2x - 4) - 3) - 1) - 3)/(1(1sin(3\u03c0(-5x^2 - 2x - 4) - 3) - 1) - 3))^2 + 5((-1(1sin(3\u03c0(-5x^2 - 2x - 4) - 3) - 1) - 3)/(1(1sin(3\u03c0(-5x^2 - 2x - 4) - 3) - 1) - 3)) - 5) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "936", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1|(2|(1|(-2x^2 + 3x - 3) + 1| - 3) + 1| - 3) - 3|)^2 + 5(-1|(2|(1|(-2x^2 + 3x - 3) + 1| - 3) + 1| - 3) - 3|) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0(2|((3(3|((1x + 3)/(2x - 3)) - 3|) + 3)/(1(3|((1x + 3)/(2x - 3)) - 3|))) + 3| + 3) - 3) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(3|(3|(3(-3x^2 + 3x - 1)^2 - 2(-3x^2 + 3x - 1) + 1) - 1| - 1) - 3| - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(-1|((3(-2|((1x + 1)/(3x - 2))| + 1) + 2)/(-3(-2|((1x + 1)/(3x - 2))| + 1) + 4))| + 1)^2 + 5(-1|((3(-2|((1x + 1)/(3x - 2))| + 1) + 2)/(-3(-2|((1x + 1)/(3x - 2))| + 1) + 4))| + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-1|(-1|(-1|(1cos(2\u03c0x - 2) + 1) - 2| + 2) + 2|) - 1| + 3) + 2)/(2(-1|(-1|(-1|(1cos(2\u03c0x - 2) + 1) - 2| + 2) + 2|) - 1| + 3) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-1|((3((-1(4x^2 + 2x - 3) - 1)/(-1(4x^2 + 2x - 3) + 2)) - 3)/(-1((-1(4x^2 + 2x - 3) - 1)/(-1(4x^2 + 2x - 3) + 2)))) - 3| + 3) - 2)/(2(-1|((3((-1(4x^2 + 2x - 3) - 1)/(-1(4x^2 + 2x - 3) + 2)) - 3)/(-1((-1(4x^2 + 2x - 3) - 1)/(-1(4x^2 + 2x - 3) + 2)))) - 3| + 3) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-2|(-1(2cos(2\u03c0(3x^2 + 3x + 3) - 1))^2 + 3(2cos(2\u03c0(3x^2 + 3x + 3) - 1)) + 4) + 3| - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-2(-3cos(3\u03c0(-1(2x^2 - 2x - 2) - 4) - 1) + 1)^2 + 5(-3cos(3\u03c0(-1(2x^2 - 2x - 2) - 4) - 1) + 1) + 2)^2 + 5(-2(-3cos(3\u03c0(-1(2x^2 - 2x - 2) - 4) - 1) + 1)^2 + 5(-3cos(3\u03c0(-1(2x^2 - 2x - 2) - 4) - 1) + 1) + 2) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "654", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-1(-2cos(2\u03c0(-4((2x + 3)/(-2x - 2)) + 1) + 3))^2 - 5(-2cos(2\u03c0(-4((2x + 3)/(-2x - 2)) + 1) + 3)) - 5) + 2| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(1|(3sin(2\u03c0(-5(2x^2 - 5x) + 1) + 2) - 1) - 2| - 2) - 1)/(-2(1|(3sin(2\u03c0(-5(2x^2 - 5x) + 1) + 2) - 1) - 2| - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "615", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3|(-1(-1|(1|(-3|x - 3| + 3) - 3|)| - 3) - 3) - 1| + 2 where -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 number of x-intercepts of the function f(x) = -3sin(3\u03c0(1(-2|(-5(-5x^2 - 2x + 2) + 4) - 1| - 1)^2 + 2(-2|(-5(-5x^2 - 2x + 2) + 4) - 1| - 1) + 4)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "455", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0(-5(-5((-2(3|x + 2| + 3) - 3)/(-2(3|x + 2| + 3) + 3)) - 4) - 3) - 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "92", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2((3(-3|((-3(3sin(1\u03c0x - 3) + 3) - 1)/(1(3sin(1\u03c0x - 3) + 3))) + 3| + 3) + 3)/(-1(-3|((-3(3sin(1\u03c0x - 3) + 3) - 1)/(1(3sin(1\u03c0x - 3) + 3))) + 3| + 3) + 3)) + 1)/(-2((3(-3|((-3(3sin(1\u03c0x - 3) + 3) - 1)/(1(3sin(1\u03c0x - 3) + 3))) + 3| + 3) + 3)/(-1(-3|((-3(3sin(1\u03c0x - 3) + 3) - 1)/(1(3sin(1\u03c0x - 3) + 3))) + 3| + 3) + 3)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3((-2(3(-1(-3|x + 1| - 2)^2 - 3(-3|x + 1| - 2) + 2) + 4) + 2)/(3(3(-1(-3|x + 1| - 2)^2 - 3(-3|x + 1| - 2) + 2) + 4) - 2))^2 + 2((-2(3(-1(-3|x + 1| - 2)^2 - 3(-3|x + 1| - 2) + 2) + 4) + 2)/(3(3(-1(-3|x + 1| - 2)^2 - 3(-3|x + 1| - 2) + 2) + 4) - 2)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5((1(-1(-1(3cos(3\u03c0x + 1) + 2)^2 - 3(3cos(3\u03c0x + 1) + 2) + 2)^2 + 4(-1(3cos(3\u03c0x + 1) + 2)^2 - 3(3cos(3\u03c0x + 1) + 2) + 2) - 1) - 1)/(2(-1(-1(3cos(3\u03c0x + 1) + 2)^2 - 3(3cos(3\u03c0x + 1) + 2) + 2)^2 + 4(-1(3cos(3\u03c0x + 1) + 2)^2 - 3(3cos(3\u03c0x + 1) + 2) + 2) - 1) - 1))^2 - 5((1(-1(-1(3cos(3\u03c0x + 1) + 2)^2 - 3(3cos(3\u03c0x + 1) + 2) + 2)^2 + 4(-1(3cos(3\u03c0x + 1) + 2)^2 - 3(3cos(3\u03c0x + 1) + 2) + 2) - 1) - 1)/(2(-1(-1(3cos(3\u03c0x + 1) + 2)^2 - 3(3cos(3\u03c0x + 1) + 2) + 2)^2 + 4(-1(3cos(3\u03c0x + 1) + 2)^2 - 3(3cos(3\u03c0x + 1) + 2) + 2) - 1) - 1)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "155", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0(-2|(-2(-1((1x + 3)/(3x + 1)))^2 + 3(-1((1x + 3)/(3x + 1))) + 3) + 2| - 2) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "129", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(5((3(1cos(3\u03c0((-2x + 3)/(3x + 1)) + 3)) - 1)/(3(1cos(3\u03c0((-2x + 3)/(3x + 1)) + 3))))) + 1)/(2(5((3(1cos(3\u03c0((-2x + 3)/(3x + 1)) + 3)) - 1)/(3(1cos(3\u03c0((-2x + 3)/(3x + 1)) + 3))))) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-3e^(1(-3|(2(-2|x - 3| + 2)^2 + 5(-2|x - 3| + 2) + 1) - 3| + 1))) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-1|((-2(-2((1x + 3)/(-3x + 1))^2 - 4((1x + 3)/(-3x + 1)) + 1) - 2)/(3(-2((1x + 3)/(-3x + 1))^2 - 4((1x + 3)/(-3x + 1)) + 1) - 2)) + 2| + 3) - 2)/(2(-1|((-2(-2((1x + 3)/(-3x + 1))^2 - 4((1x + 3)/(-3x + 1)) + 1) - 2)/(3(-2((1x + 3)/(-3x + 1))^2 - 4((1x + 3)/(-3x + 1)) + 1) - 2)) + 2| + 3)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-3(2(-3cos(3\u03c0(-4x + 3)) + 2)^2 + 5(-3cos(3\u03c0(-4x + 3)) + 2))^2 - 3(2(-3cos(3\u03c0(-4x + 3)) + 2)^2 + 5(-3cos(3\u03c0(-4x + 3)) + 2)) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0(-1(2|((-3(-5x - 2) + 2)/(-3(-5x - 2))) + 1|)^2 + 3(2|((-3(-5x - 2) + 2)/(-3(-5x - 2))) + 1|) - 1) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(2(-1(-2|(-2x) - 3| + 1)^2 + 4(-2|(-2x) - 3| + 1)) + 1) + 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(3(-2(-3sin(2\u03c0(4x + 2) + 3) - 1)^2 + 3(-3sin(2\u03c0(4x + 2) + 3) - 1) + 1) + 2) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-4(1(-2((-2x + 3)/(3x + 3))^2 + 2((-2x + 3)/(3x + 3)) + 3) + 2)^2 + 5(1(-2((-2x + 3)/(3x + 3))^2 + 2((-2x + 3)/(3x + 3)) + 3) + 2) + 2) - 2)/(-3(-4(1(-2((-2x + 3)/(3x + 3))^2 + 2((-2x + 3)/(3x + 3)) + 3) + 2)^2 + 5(1(-2((-2x + 3)/(3x + 3))^2 + 2((-2x + 3)/(3x + 3)) + 3) + 2) + 2) + 1) where -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 number of x-intercepts of the function f(x) = (2((-2(-2(2|(-1x^2 + 4x - 2) + 2| - 3)^2 + 4(2|(-1x^2 + 4x - 2) + 2| - 3) - 3))/(1(-2(2|(-1x^2 + 4x - 2) + 2| - 3)^2 + 4(2|(-1x^2 + 4x - 2) + 2| - 3) - 3) + 3)) - 3)/(2((-2(-2(2|(-1x^2 + 4x - 2) + 2| - 3)^2 + 4(2|(-1x^2 + 4x - 2) + 2| - 3) - 3))/(1(-2(2|(-1x^2 + 4x - 2) + 2| - 3)^2 + 4(2|(-1x^2 + 4x - 2) + 2| - 3) - 3) + 3)) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(2sin(3\u03c0((2(-3|(3|x + 1| + 2) - 3| + 3) + 3)/(3(-3|(3|x + 1| + 2) - 3| + 3) + 1)) + 1) - 2)^2 - 5(2sin(3\u03c0((2(-3|(3|x + 1| + 2) - 3| + 3) + 3)/(3(-3|(3|x + 1| + 2) - 3| + 3) + 1)) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "24", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(3sin(1\u03c0(5(4(3x)^2 - 2(3x) + 4) - 3) + 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1493", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(1(2((1(5x^2 - 1))/(-1(5x^2 - 1) + 2)) - 5)^2 + 1(2((1(5x^2 - 1))/(-1(5x^2 - 1) + 2)) - 5) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3((1(-2sin(1\u03c0(-2|(2x^2 + 3x - 5) + 1|) + 2) - 2))/(-1(-2sin(1\u03c0(-2|(2x^2 + 3x - 5) + 1|) + 2) - 2) + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "355", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(-3|(-2(3|(-1x - 1) - 3| - 2) + 3) - 3|) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-4(-1(5(1|x - 1| - 1) + 3)^2 + 5(5(1|x - 1| - 1) + 3) - 2)^2 - 2(-1(5(1|x - 1| - 1) + 3)^2 + 5(5(1|x - 1| - 1) + 3) - 2) + 5) + 3)/(-1(-4(-1(5(1|x - 1| - 1) + 3)^2 + 5(5(1|x - 1| - 1) + 3) - 2)^2 - 2(-1(5(1|x - 1| - 1) + 3)^2 + 5(5(1|x - 1| - 1) + 3) - 2) + 5) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-1|((3(-1(-1x^2 - 1x + 4)^2 - 1(-1x^2 - 1x + 4) + 4) + 2)/(2(-1(-1x^2 - 1x + 4)^2 - 1(-1x^2 - 1x + 4) + 4) - 1)) - 1| + 3) - 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-3((-3(4(-2|x - 3|)) - 1)/(3(4(-2|x - 3|)) - 2))^2 + 5((-3(4(-2|x - 3|)) - 1)/(3(4(-2|x - 3|)) - 2)) + 1) + 1| + 1 have 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 number of x-intercepts of the function f(x) = -1((-2(-1(5(-1x^2 - 3x + 1)) + 4) - 3)/(3(-1(5(-1x^2 - 3x + 1)) + 4) + 3))^2 + 4((-2(-1(5(-1x^2 - 3x + 1)) + 4) - 3)/(3(-1(5(-1x^2 - 3x + 1)) + 4) + 3)) + 2 where -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 number of x-intercepts of the function f(x) = -4(-2|(-4(1(2|x|)^2 - 5(2|x|) - 2)^2 - 5(1(2|x|)^2 - 5(2|x|) - 2) - 4) + 2| + 2) - 2 where -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 number of x-intercepts of the function f(x) = -1(3|(1(2|((-2x - 3)/(-1x - 1)) - 1| - 2)^2 + 5(2|((-2x - 3)/(-1x - 1)) - 1| - 2)) - 3|)^2 + 4(3|(1(2|((-2x - 3)/(-1x - 1)) - 1| - 2)^2 + 5(2|((-2x - 3)/(-1x - 1)) - 1| - 2)) - 3|) + 3 where -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 number of x-intercepts of the function f(x) = 1|(-3|(-1|(-4(-4x + 5) + 5) - 3| + 1) + 2| - 2) + 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-1(3(1|(-2x^2 - 2x + 2)| - 3)^2 + 1(1|(-2x^2 - 2x + 2)| - 3) - 5) + 5) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(-2|(1(-3(4x)^2 + 1(4x) - 5) + 3) - 3| - 2) + 1) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1253", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(2sin(1\u03c0(-4(2(-3|x - 2| - 1)^2 + 5(-3|x - 2| - 1) - 1)^2 - 5(2(-3|x - 2| - 1)^2 + 5(-3|x - 2| - 1) - 1) - 2) - 2))^2 - 4(2sin(1\u03c0(-4(2(-3|x - 2| - 1)^2 + 5(-3|x - 2| - 1) - 1)^2 - 5(2(-3|x - 2| - 1)^2 + 5(-3|x - 2| - 1) - 1) - 2) - 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "379", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-3(1((3(3x^2 - 4x - 4) - 3)/(-3(3x^2 - 4x - 4) - 1)) - 5)^2 - 2(1((3(3x^2 - 4x - 4) - 3)/(-3(3x^2 - 4x - 4) - 1)) - 5))^2 + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(5(2(3cos(3\u03c0((-1x - 3)/(-3x + 2)) + 2) - 1)^2 - 2(3cos(3\u03c0((-1x - 3)/(-3x + 2)) + 2) - 1) - 5)^2 + 3(2(3cos(3\u03c0((-1x - 3)/(-3x + 2)) + 2) - 1)^2 - 2(3cos(3\u03c0((-1x - 3)/(-3x + 2)) + 2) - 1) - 5) - 5) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "67", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(-2(-4(-1(3x - 3) + 5) - 1)^2 - 5(-4(-1(3x - 3) + 5) - 1) - 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1566", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(1(-3|(-5(-2|x + 1| + 1) - 5) - 1|) + 3)^2 - 2(1(-3|(-5(-2|x + 1| + 1) - 5) - 1|) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2((-3(2|(1(1x - 3)^2 - 3(1x - 3)) + 3| - 1) + 2)/(2(2|(1(1x - 3)^2 - 3(1x - 3)) + 3| - 1) + 3))^2 - 2((-3(2|(1(1x - 3)^2 - 3(1x - 3)) + 3| - 1) + 2)/(2(2|(1(1x - 3)^2 - 3(1x - 3)) + 3| - 1) + 3)) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(4(-2(-5(3|x - 3| - 3) - 4) - 2) + 3) - 3| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-3e^(2(2(-3(-1|x + 1| + 3) + 2)^2 - 5(-3(-1|x + 1| + 3) + 2))) + 3) + 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-4(1cos(1\u03c0(-1(-2x^2 - 1x) - 1) + 3) - 2)^2 - 5(1cos(1\u03c0(-1(-2x^2 - 1x) - 1) + 3) - 2) + 4)^2 + 4(-4(1cos(1\u03c0(-1(-2x^2 - 1x) - 1) + 3) - 2)^2 - 5(1cos(1\u03c0(-1(-2x^2 - 1x) - 1) + 3) - 2) + 4) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "522", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1(-5(-3|((-2x + 1)/(1x)) + 3| + 3) - 2)^2 - 3(-5(-3|((-2x + 1)/(1x)) + 3| + 3) - 2))^2 + 1(1(-5(-3|((-2x + 1)/(1x)) + 3| + 3) - 2)^2 - 3(-5(-3|((-2x + 1)/(1x)) + 3| + 3) - 2)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(3e^(1(-5((2(1x + 4) - 1)/(-1(1x + 4) - 3)) - 5)) - 1) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(4(-3sin(2\u03c0(-3((-1x)/(-2x + 3))^2 - 5((-1x)/(-2x + 3)) - 3) - 1) + 1) - 3) + 1)/(-2(4(-3sin(2\u03c0(-3((-1x)/(-2x + 3))^2 - 5((-1x)/(-2x + 3)) - 3) - 1) + 1) - 3) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-2|(5(2(-2x + 5)^2 + 1(-2x + 5) - 5) + 2) + 3| + 2) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(-4(-2((2(2sin(2\u03c0x + 1) - 1) + 3)/(1(2sin(2\u03c0x + 1) - 1)))^2 - 3((2(2sin(2\u03c0x + 1) - 1) + 3)/(1(2sin(2\u03c0x + 1) - 1))) - 1) - 1) + 1| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-1sin(2\u03c0(-1|(-5(1|x - 1| - 3) + 3)| + 2) - 1))^2 + 2(-1sin(2\u03c0(-1|(-5(1|x - 1| - 3) + 3)| + 2) - 1)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-3|((2(1e^(2((2x + 1)/(3x - 2))) - 3) - 3)/(-2(1e^(2((2x + 1)/(3x - 2))) - 3) - 2)) + 2| + 3) + 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(2cos(2\u03c0(-1(-1|(2x^2 - 5x + 2) - 3| + 3) - 1) - 1) + 2))/(-1(2cos(2\u03c0(-1(-1|(2x^2 - 5x + 2) - 3| + 3) - 1) - 1) + 2) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "394", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(-2sin(2\u03c0(-3|(-1|(3|x - 1| + 3) + 3| + 2) + 2| - 1) + 3) - 1) + 1)/(2(-2sin(2\u03c0(-3|(-1|(3|x - 1| + 3) + 3| + 2) + 2| - 1) + 3) - 1) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2((2(3|(5(1cos(2\u03c0x - 3)) + 4) + 1| + 1) + 1)/(-3(3|(5(1cos(2\u03c0x - 3)) + 4) + 1| + 1) + 2)) + 2)/(2((2(3|(5(1cos(2\u03c0x - 3)) + 4) + 1| + 1) + 1)/(-3(3|(5(1cos(2\u03c0x - 3)) + 4) + 1| + 1) + 2)) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4((-3(5(1(3x + 1)^2 - 4(3x + 1) - 5)^2 - 5(1(3x + 1)^2 - 4(3x + 1) - 5) - 5) - 1)/(1(5(1(3x + 1)^2 - 4(3x + 1) - 5)^2 - 5(1(3x + 1)^2 - 4(3x + 1) - 5) - 5) - 3)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2(2(-4(3|(-1|x - 3| + 2) - 1|) - 3) + 4)^2 - 4(2(-4(3|(-1|x - 3| + 2) - 1|) - 3) + 4) + 5 have 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 number of x-intercepts of the function f(x) = 2((3(-2|(1sin(3\u03c0((3x - 3)/(2x - 3))) - 1) + 1| + 1) - 2)/(-3(-2|(1sin(3\u03c0((3x - 3)/(2x - 3))) - 1) + 1| + 1) + 1)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(5(-4((-3(-1x^2 + 3x + 4) - 1)/(-3(-1x^2 + 3x + 4) - 3)) - 2) + 4) - 1) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-1(-3|(1|(-2cos(3\u03c0x) + 2) + 1|) - 1| + 2)^2 + 1(-3|(1|(-2cos(3\u03c0x) + 2) + 1|) - 1| + 2) + 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(3\u03c0(-3(3(5((2x + 1)/(1x - 2)) + 3) - 5)^2 + 5(3(5((2x + 1)/(1x - 2)) + 3) - 5) - 3) + 3) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1195", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(-4((2((-2(-3|x + 1| - 3) - 1)/(-2(-3|x + 1| - 3) + 3)) - 3)/(-1((-2(-3|x + 1| - 3) - 1)/(-2(-3|x + 1| - 3) + 3)) - 1))^2 + 2((2((-2(-3|x + 1| - 3) - 1)/(-2(-3|x + 1| - 3) + 3)) - 3)/(-1((-2(-3|x + 1| - 3) - 1)/(-2(-3|x + 1| - 3) + 3)) - 1)) - 1)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(-3sin(2\u03c0(1(-1(5x^2 + 4x - 3)^2 - 4)^2 + 2(-1(5x^2 + 4x - 3)^2 - 4) + 4))) - 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2(-2cos(3\u03c0((2((3(-3x + 4) - 2)/(-2(-3x + 4) - 2)) - 1)/(1((3(-3x + 4) - 2)/(-2(-3x + 4) - 2)) - 3)) - 2) - 1)^2 - 4(-2cos(3\u03c0((2((3(-3x + 4) - 2)/(-2(-3x + 4) - 2)) - 1)/(1((3(-3x + 4) - 2)/(-2(-3x + 4) - 2)) - 3)) - 2) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1(-3cos(2\u03c0((-1(2(-2|x - 1| + 3) + 3))/(-1(2(-2|x - 1| + 3) + 3) + 2)) - 1))^2 - 4(-3cos(2\u03c0((-1(2(-2|x - 1| + 3) + 3))/(-1(2(-2|x - 1| + 3) + 3) + 2)) - 1)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-5(3cos(1\u03c0(-3(3|x| + 1)^2 - 5(3|x| + 1) + 3) + 1) - 2)^2 + 2(3cos(1\u03c0(-3(3|x| + 1)^2 - 5(3|x| + 1) + 3) + 1) - 2) + 5) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1285", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2(4(-3sin(3\u03c0(5x - 4) + 2) + 3)^2 - 1(-3sin(3\u03c0(5x - 4) + 2) + 3) - 3)^2 + 5(4(-3sin(3\u03c0(5x - 4) + 2) + 3)^2 - 1(-3sin(3\u03c0(5x - 4) + 2) + 3) - 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "231", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(2\u03c0(5(-5((-3(4x + 4) - 2)/(-1(4x + 4) - 3)) - 5) - 3) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "321", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|(-1(-1(2(3x - 4) - 4)^2 + 1(2(3x - 4) - 4) + 3) - 1) - 1| + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(5(-2(-2|(1sin(2\u03c0x + 1) + 2) + 1| + 3)^2 - 3(-2|(1sin(2\u03c0x + 1) + 2) + 1| + 3) + 4) + 2) + 2)/(2(5(-2(-2|(1sin(2\u03c0x + 1) + 2) + 1| + 3)^2 - 3(-2|(1sin(2\u03c0x + 1) + 2) + 1| + 3) + 4) + 2) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1((-1(5(-3(1sin(3\u03c0x - 3) + 1)^2 + 1(1sin(3\u03c0x - 3) + 1)) + 4) - 3)/(-1(5(-3(1sin(3\u03c0x - 3) + 1)^2 + 1(1sin(3\u03c0x - 3) + 1)) + 4) - 2))^2 + 5((-1(5(-3(1sin(3\u03c0x - 3) + 1)^2 + 1(1sin(3\u03c0x - 3) + 1)) + 4) - 3)/(-1(5(-3(1sin(3\u03c0x - 3) + 1)^2 + 1(1sin(3\u03c0x - 3) + 1)) + 4) - 2)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-2(3((1(-5x^2 - 5x + 1) - 1)/(-2(-5x^2 - 5x + 1) + 1))^2 - 2((1(-5x^2 - 5x + 1) - 1)/(-2(-5x^2 - 5x + 1) + 1)) - 2)^2 - 4(3((1(-5x^2 - 5x + 1) - 1)/(-2(-5x^2 - 5x + 1) + 1))^2 - 2((1(-5x^2 - 5x + 1) - 1)/(-2(-5x^2 - 5x + 1) + 1)) - 2) + 1)| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-1(-3|((1(1|x + 3| - 1) + 3)/(1(1|x + 3| - 1) + 1)) - 2|)^2 - 5(-3|((1(1|x + 3| - 1) + 3)/(1(1|x + 3| - 1) + 1)) - 2|) + 3)^2 - 5(-1(-3|((1(1|x + 3| - 1) + 3)/(1(1|x + 3| - 1) + 1)) - 2|)^2 - 5(-3|((1(1|x + 3| - 1) + 3)/(1(1|x + 3| - 1) + 1)) - 2|) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(1sin(1\u03c0(3|(1|(-1x^2 - 5x) + 2| + 3) + 3| + 1) + 2)) + 1)/(-1(1sin(1\u03c0(3|(1|(-1x^2 - 5x) + 2| + 3) + 3| + 1) + 2)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "306", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(3(3sin(3\u03c0(-1(-1|x| - 2) + 5)) + 2)^2 - 5(3sin(3\u03c0(-1(-1|x| - 2) + 5)) + 2) - 4) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1((2((-1(5(-2|x - 3| + 1) - 2) - 2)/(-2(5(-2|x - 3| + 1) - 2) - 3)) - 2)/(3((-1(5(-2|x - 3| + 1) - 2) - 2)/(-2(5(-2|x - 3| + 1) - 2) - 3))))^2 + 3((2((-1(5(-2|x - 3| + 1) - 2) - 2)/(-2(5(-2|x - 3| + 1) - 2) - 3)) - 2)/(3((-1(5(-2|x - 3| + 1) - 2) - 2)/(-2(5(-2|x - 3| + 1) - 2) - 3)))) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3cos(1\u03c0((-2(5(3|(-2|x - 3|) + 3| - 3) + 3) - 2)/(-2(5(3|(-2|x - 3|) + 3| - 3) + 3) + 3)) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4((-3(-2(-4(-2cos(1\u03c0x + 2) + 2)^2 - 4(-2cos(1\u03c0x + 2) + 2) + 2) - 4) - 3)/(-3(-2(-4(-2cos(1\u03c0x + 2) + 2)^2 - 4(-2cos(1\u03c0x + 2) + 2) + 2) - 4) + 1))^2 - 5((-3(-2(-4(-2cos(1\u03c0x + 2) + 2)^2 - 4(-2cos(1\u03c0x + 2) + 2) + 2) - 4) - 3)/(-3(-2(-4(-2cos(1\u03c0x + 2) + 2)^2 - 4(-2cos(1\u03c0x + 2) + 2) + 2) - 4) + 1)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4((-3((1(-2(2|x + 1| - 1)^2 + 4(2|x + 1| - 1)) - 2)/(1(-2(2|x + 1| - 1)^2 + 4(2|x + 1| - 1)) + 1)) - 1)/(-1((1(-2(2|x + 1| - 1)^2 + 4(2|x + 1| - 1)) - 2)/(1(-2(2|x + 1| - 1)^2 + 4(2|x + 1| - 1)) + 1)) + 3))^2 - 3((-3((1(-2(2|x + 1| - 1)^2 + 4(2|x + 1| - 1)) - 2)/(1(-2(2|x + 1| - 1)^2 + 4(2|x + 1| - 1)) + 1)) - 1)/(-1((1(-2(2|x + 1| - 1)^2 + 4(2|x + 1| - 1)) - 2)/(1(-2(2|x + 1| - 1)^2 + 4(2|x + 1| - 1)) + 1)) + 3)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1(3(-1(-2x^2 + 4x - 4) - 2)^2 - 3(-1(-2x^2 + 4x - 4) - 2) + 2) - 1)^2 + 1(1(3(-1(-2x^2 + 4x - 4) - 2)^2 - 3(-1(-2x^2 + 4x - 4) - 2) + 2) - 1) - 4 where -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 number of x-intercepts of the function f(x) = 3|((-1(-3(3(-1x + 1) + 1)^2 - 5(3(-1x + 1) + 1) + 2) - 2)/(1(-3(3(-1x + 1) + 1)^2 - 5(3(-1x + 1) + 1) + 2) - 3)) - 1| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(2|(-3(-2|(-2x + 5)| + 2)^2 + 2(-2|(-2x + 5)| + 2) - 1) + 2| - 3) + 3)/(2(2|(-3(-2|(-2x + 5)| + 2)^2 + 2(-2|(-2x + 5)| + 2) - 1) + 2| - 3) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|((1((-1(3cos(3\u03c0(-2x - 5) + 2) + 1))/(3(3cos(3\u03c0(-2x - 5) + 2) + 1) + 2)) - 3)/(-1((-1(3cos(3\u03c0(-2x - 5) + 2) + 1))/(3(3cos(3\u03c0(-2x - 5) + 2) + 1) + 2)) - 3)) - 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "98", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-1(2|(-2sin(2\u03c0(-3x^2 + 2x + 3) + 2) - 2)| + 1)^2 + 4(2|(-2sin(2\u03c0(-3x^2 + 2x + 3) + 2) - 2)| + 1) - 1) + 2)/(2(-1(2|(-2sin(2\u03c0(-3x^2 + 2x + 3) + 2) - 2)| + 1)^2 + 4(2|(-2sin(2\u03c0(-3x^2 + 2x + 3) + 2) - 2)| + 1) - 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|((-2((2(2cos(3\u03c0(-1|x + 2|) - 2)) - 3)/(3(2cos(3\u03c0(-1|x + 2|) - 2)) + 3)) + 1)/(3((2(2cos(3\u03c0(-1|x + 2|) - 2)) - 3)/(3(2cos(3\u03c0(-1|x + 2|) - 2)) + 3)) + 3)) + 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1e^(-1(1((-1(-5(1|x| + 1)^2 + 1(1|x| + 1) + 5) + 2)/(-1(-5(1|x| + 1)^2 + 1(1|x| + 1) + 5)))^2 - 2((-1(-5(1|x| + 1)^2 + 1(1|x| + 1) + 5) + 2)/(-1(-5(1|x| + 1)^2 + 1(1|x| + 1) + 5))) - 5)) - 2 where -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 number of x-intercepts of the function f(x) = -2|(-3(3(2|(-1x^2 + 3x + 4) - 1| - 1) + 5) + 5) + 2| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(1(3(2(-3sin(3\u03c0x + 1) + 1)^2 - 4(-3sin(3\u03c0x + 1) + 1) - 5)^2 - 4(2(-3sin(3\u03c0x + 1) + 1)^2 - 4(-3sin(3\u03c0x + 1) + 1) - 5) + 3)^2 - 2(3(2(-3sin(3\u03c0x + 1) + 1)^2 - 4(-3sin(3\u03c0x + 1) + 1) - 5)^2 - 4(2(-3sin(3\u03c0x + 1) + 1)^2 - 4(-3sin(3\u03c0x + 1) + 1) - 5) + 3) - 3) - 2)/(2(1(3(2(-3sin(3\u03c0x + 1) + 1)^2 - 4(-3sin(3\u03c0x + 1) + 1) - 5)^2 - 4(2(-3sin(3\u03c0x + 1) + 1)^2 - 4(-3sin(3\u03c0x + 1) + 1) - 5) + 3)^2 - 2(3(2(-3sin(3\u03c0x + 1) + 1)^2 - 4(-3sin(3\u03c0x + 1) + 1) - 5)^2 - 4(2(-3sin(3\u03c0x + 1) + 1)^2 - 4(-3sin(3\u03c0x + 1) + 1) - 5) + 3) - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "23", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-2|(2(4(5x) + 5)^2 - 2(4(5x) + 5) - 5)| - 1) + 3)/(3(-2|(2(4(5x) + 5)^2 - 2(4(5x) + 5) - 5)| - 1) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(5(3cos(3\u03c0(-5(-5x^2 + 1x + 5) + 5) - 2) - 3)^2 + 2(3cos(3\u03c0(-5(-5x^2 + 1x + 5) + 5) - 2) - 3) + 2)^2 + 1(5(3cos(3\u03c0(-5(-5x^2 + 1x + 5) + 5) - 2) - 3)^2 + 2(3cos(3\u03c0(-5(-5x^2 + 1x + 5) + 5) - 2) - 3) + 2) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "344", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(1|(-2|(1(-2|x - 2| + 2)^2 - 2(-2|x - 2| + 2) - 2) + 1| - 2) + 2|) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(-1|(3sin(1\u03c0(2|(-3|x + 1| - 1) + 2|) - 1) - 1) + 3| + 2) - 1| + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(4(1|(-5(3cos(1\u03c0x) - 1)^2 + 1(3cos(1\u03c0x) - 1) + 1)|)^2 + 4(1|(-5(3cos(1\u03c0x) - 1)^2 + 1(3cos(1\u03c0x) - 1) + 1)|) - 1) + 3)/(-3(4(1|(-5(3cos(1\u03c0x) - 1)^2 + 1(3cos(1\u03c0x) - 1) + 1)|)^2 + 4(1|(-5(3cos(1\u03c0x) - 1)^2 + 1(3cos(1\u03c0x) - 1) + 1)|) - 1) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "66", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1(-2cos(3\u03c0((2(-1(1|x - 1| - 3)^2 + 5(1|x - 1| - 3) - 4) + 1)/(2(-1(1|x - 1| - 3)^2 + 5(1|x - 1| - 3) - 4))) - 1) + 3)^2 + 4(-2cos(3\u03c0((2(-1(1|x - 1| - 3)^2 + 5(1|x - 1| - 3) - 4) + 1)/(2(-1(1|x - 1| - 3)^2 + 5(1|x - 1| - 3) - 4))) - 1) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "132", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5((1((1(2((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 2) - 2)/(1(2((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 2) - 3)) - 3)/(-1((1(2((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 2) - 2)/(1(2((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 2) - 3)) + 2))^2 + 1((1((1(2((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 2) - 2)/(1(2((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 2) - 3)) - 3)/(-1((1(2((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 2) - 2)/(1(2((-2x - 2)/(1x))^2 + 5((-2x - 2)/(1x)) + 2) - 3)) + 2)) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-1|((-1(-3cos(3\u03c0((2x + 2)/(-2x + 1)) - 1)) - 3)/(2(-3cos(3\u03c0((2x + 2)/(-2x + 1)) - 1)) + 3)) - 2| + 1) + 1)/(-1(-1|((-1(-3cos(3\u03c0((2x + 2)/(-2x + 1)) - 1)) - 3)/(2(-3cos(3\u03c0((2x + 2)/(-2x + 1)) - 1)) + 3)) - 2| + 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-1|(2|(-1sin(2\u03c0((-3x + 1)/(2x + 3))) - 2) + 3| + 3)| + 2)| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1(-2(1(-3|x + 3| + 1) + 1) - 4) - 1)^2 - 5(1(-2(1(-3|x + 3| + 1) + 1) - 4) - 1) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(2sin(1\u03c0(-2|((-3(3x - 4) - 3)/(-3(3x - 4) - 2)) - 2|)) + 1) - 1| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|((3(-5(1(2x + 2))^2 - 3(1(2x + 2)) + 4) - 1)/(3(-5(1(2x + 2))^2 - 3(1(2x + 2)) + 4) - 2)) + 3| + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(1cos(2\u03c0(-4((2(-5x^2 - 5x - 1) + 1)/(1(-5x^2 - 5x - 1) - 2))^2 - 5((2(-5x^2 - 5x - 1) + 1)/(1(-5x^2 - 5x - 1) - 2)) - 5) + 1)) - 1)/(-2(1cos(2\u03c0(-4((2(-5x^2 - 5x - 1) + 1)/(1(-5x^2 - 5x - 1) - 2))^2 - 5((2(-5x^2 - 5x - 1) + 1)/(1(-5x^2 - 5x - 1) - 2)) - 5) + 1)) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-3sin(2\u03c0((-2((-2((-1x + 1)/(-2x)) + 2)/(2((-1x + 1)/(-2x)) + 2)) - 2)/(3((-2((-1x + 1)/(-2x)) + 2)/(2((-1x + 1)/(-2x)) + 2)) - 2))) - 1) - 1)/(3(-3sin(2\u03c0((-2((-2((-1x + 1)/(-2x)) + 2)/(2((-1x + 1)/(-2x)) + 2)) - 2)/(3((-2((-1x + 1)/(-2x)) + 2)/(2((-1x + 1)/(-2x)) + 2)) - 2))) - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "25", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3sin(3\u03c0((2(-1(-2((-2x - 2)/(2x)) + 5)^2 + 2(-2((-2x - 2)/(2x)) + 5) + 2))/(-2(-1(-2((-2x - 2)/(2x)) + 5)^2 + 2(-2((-2x - 2)/(2x)) + 5) + 2) - 3))) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(1cos(2\u03c0(1|((1(1x^2 - 4x - 5) + 3)/(1(1x^2 - 4x - 5) + 2)) + 3| + 1) + 3) + 3) - 3| have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "13", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(5(-5(2cos(2\u03c0(4x - 1) - 3) + 1) - 3)^2 - 2(-5(2cos(2\u03c0(4x - 1) - 3) + 1) - 3) - 3) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1e^(1((2(-4(-1(-2x - 1)^2 - 2(-2x - 1) + 2)^2 - 5(-1(-2x - 1)^2 - 2(-2x - 1) + 2) + 5) + 1)/(-1(-4(-1(-2x - 1)^2 - 2(-2x - 1) + 2)^2 - 5(-1(-2x - 1)^2 - 2(-2x - 1) + 2) + 5) - 2))) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-5(2sin(2\u03c0(2(-3|x + 2| - 2)^2 + 2(-3|x + 2| - 2) - 1) + 2) + 1) - 2) + 1)/(-1(-5(2sin(2\u03c0(2(-3|x + 2| - 2)^2 + 2(-3|x + 2| - 2) - 1) + 2) + 1) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "153", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1sin(3\u03c0(1|((3((2((-2x + 1)/(-2x)) + 1)/(-1((-2x + 1)/(-2x)) + 2)) - 2)/(1((2((-2x + 1)/(-2x)) + 1)/(-1((-2x + 1)/(-2x)) + 2)) + 1)) - 1| - 3)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(3sin(3\u03c0(3|(2|(-3|x - 2| - 1)| + 2) + 1| - 2) - 2) + 3)^2 + 3(3sin(3\u03c0(3|(2|(-3|x - 2| - 1)| + 2) + 1| - 2) - 2) + 3) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "940", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-2(3(-2|(1sin(1\u03c0x + 1) + 3) - 3|)^2 - 2(-2|(1sin(1\u03c0x + 1) + 3) - 3|) - 4) + 3)^2 - 5(-2(3(-2|(1sin(1\u03c0x + 1) + 3) - 3|)^2 - 2(-2|(1sin(1\u03c0x + 1) + 3) - 3|) - 4) + 3) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-3|((1(-3|(-3|x + 3| + 3) - 2| + 1) + 3)/(1(-3|(-3|x + 3| + 3) - 2| + 1) + 2)) + 3|) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-3sin(1\u03c0(1((-3(-1x^2 - 3x) - 1)/(1(-1x^2 - 3x) + 2)) - 2)) + 3))/(3(-3sin(1\u03c0(1((-3(-1x^2 - 3x) - 1)/(1(-1x^2 - 3x) + 2)) - 2)) + 3) + 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(3sin(3\u03c0(1(3|((1x + 2)/(-3x + 2)) - 3| + 3)^2 - 5(3|((1x + 2)/(-3x + 2)) - 3| + 3) + 3) - 2) - 2))/(3(3sin(3\u03c0(1(3|((1x + 2)/(-3x + 2)) - 3| + 3)^2 - 5(3|((1x + 2)/(-3x + 2)) - 3| + 3) + 3) - 2) - 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "256", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0((1(5(-1(3|x + 1| - 2)^2 + 4(3|x + 1| - 2) - 4) + 3) - 2)/(3(5(-1(3|x + 1| - 2)^2 + 4(3|x + 1| - 2) - 4) + 3) - 1)) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "34", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(1|(-1(-2|(-1x + 1) + 1| - 1) - 3) + 1|)^2 + 1(1|(-1(-2|(-1x + 1) + 1| - 1) - 3) + 1|) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(2|(-1|(3e^(2(4x - 2)) - 2) - 1| + 2)| - 1)^2 + 4(2|(-1|(3e^(2(4x - 2)) - 2) - 1| + 2)| - 1) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-4(-3cos(3\u03c0(2|(-2x + 5) - 1| - 1) + 1) + 2) - 3) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3sin(3\u03c0(-1(-2(3(-1x^2 - 3x - 2)^2 - 3(-1x^2 - 3x - 2) - 3)) - 3) - 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1147", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(1|(5(-1|(-3x^2 - 5x - 3) + 1| + 3) - 5) + 1| - 3)^2 - 2(1|(5(-1|(-3x^2 - 5x - 3) + 1| + 3) - 5) + 1| - 3) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(1\u03c0(2(2|(1|(-1x^2 + 1x + 3) + 3|) - 1| + 1)^2 + 3(2|(1|(-1x^2 + 1x + 3) + 3|) - 1| + 1)) - 2) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1239", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|((-1(-4(2e^(1(-1x^2 + 5x + 3)) - 1)^2 + 3(2e^(1(-1x^2 + 5x + 3)) - 1) + 4) - 2)/(2(-4(2e^(1(-1x^2 + 5x + 3)) - 1)^2 + 3(2e^(1(-1x^2 + 5x + 3)) - 1) + 4) + 3)) + 2| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(2\u03c0(4(-2|(3(-2|x + 3| + 1)^2 - 4(-2|x + 3| + 1)) + 3| - 2)^2 - 2(-2|(3(-2|x + 3| + 1)^2 - 4(-2|x + 3| + 1)) + 3| - 2) - 2) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "590", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-2(-2((3(-3cos(3\u03c0(-1x^2 + 3x - 1) + 3) - 2) + 2)/(-2(-3cos(3\u03c0(-1x^2 + 3x - 1) + 3) - 2) + 3))^2 - 3((3(-3cos(3\u03c0(-1x^2 + 3x - 1) + 3) - 2) + 2)/(-2(-3cos(3\u03c0(-1x^2 + 3x - 1) + 3) - 2) + 3))) - 2)/(-2(-2((3(-3cos(3\u03c0(-1x^2 + 3x - 1) + 3) - 2) + 2)/(-2(-3cos(3\u03c0(-1x^2 + 3x - 1) + 3) - 2) + 3))^2 - 3((3(-3cos(3\u03c0(-1x^2 + 3x - 1) + 3) - 2) + 2)/(-2(-3cos(3\u03c0(-1x^2 + 3x - 1) + 3) - 2) + 3))) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "611", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1((1(3cos(2\u03c0((2(-5x^2 + 3x + 3) - 2)/(-2(-5x^2 + 3x + 3) - 2)) + 2) - 2))/(3(3cos(2\u03c0((2(-5x^2 + 3x + 3) - 2)/(-2(-5x^2 + 3x + 3) - 2)) + 2) - 2) + 1)) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(1(-1|((1(-2|x + 1|) + 3)/(-2(-2|x + 1|))) + 1| - 3)^2 + 4(-1|((1(-2|x + 1|) + 3)/(-2(-2|x + 1|))) + 1| - 3))^2 + 3(1(-1|((1(-2|x + 1|) + 3)/(-2(-2|x + 1|))) + 1| - 3)^2 + 4(-1|((1(-2|x + 1|) + 3)/(-2(-2|x + 1|))) + 1| - 3)) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-3cos(1\u03c0(3|((2((-2x + 2)/(3x + 1)) + 3)/(-3((-2x + 2)/(3x + 1)) - 2)) + 1| + 1) - 1) + 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "37", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3cos(1\u03c0((-1((2((2(-2x - 5) - 3)/(-1(-2x - 5) - 1)))/(2((2(-2x - 5) - 3)/(-1(-2x - 5) - 1)) - 3)) + 3)/(2((2((2(-2x - 5) - 3)/(-1(-2x - 5) - 1)))/(2((2(-2x - 5) - 3)/(-1(-2x - 5) - 1)) - 3)) - 1)) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "249", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4((-2(1(2|(4x - 1) - 3| - 3)^2 + 3(2|(4x - 1) - 3| - 3) - 4) + 3)/(1(1(2|(4x - 1) - 3| - 3)^2 + 3(2|(4x - 1) - 3| - 3) - 4)))^2 - 5((-2(1(2|(4x - 1) - 3| - 3)^2 + 3(2|(4x - 1) - 3| - 3) - 4) + 3)/(1(1(2|(4x - 1) - 3| - 3)^2 + 3(2|(4x - 1) - 3| - 3) - 4))) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-2e^(-1((-2(1(3x + 4) - 3) - 1)/(-1(1(3x + 4) - 3) + 3))) - 2) + 3| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2((3(4(5(-2sin(3\u03c0x - 3))^2 + 4(-2sin(3\u03c0x - 3)) - 1)^2 + 2(5(-2sin(3\u03c0x - 3))^2 + 4(-2sin(3\u03c0x - 3)) - 1) - 2) + 3)/(1(4(5(-2sin(3\u03c0x - 3))^2 + 4(-2sin(3\u03c0x - 3)) - 1)^2 + 2(5(-2sin(3\u03c0x - 3))^2 + 4(-2sin(3\u03c0x - 3)) - 1) - 2))) + 2)/(2((3(4(5(-2sin(3\u03c0x - 3))^2 + 4(-2sin(3\u03c0x - 3)) - 1)^2 + 2(5(-2sin(3\u03c0x - 3))^2 + 4(-2sin(3\u03c0x - 3)) - 1) - 2) + 3)/(1(4(5(-2sin(3\u03c0x - 3))^2 + 4(-2sin(3\u03c0x - 3)) - 1)^2 + 2(5(-2sin(3\u03c0x - 3))^2 + 4(-2sin(3\u03c0x - 3)) - 1) - 2)))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-3(4(-3cos(2\u03c0(3|x + 2| - 3)) + 1) + 2) + 1) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 5(3(3sin(2\u03c0(-1((-2x - 3)/(-1x)) + 1) + 1) + 1) - 5) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "90", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1(-3(1(3|x + 2|)^2 - 3(3|x + 2|) - 3)^2 - 5(1(3|x + 2|)^2 - 3(3|x + 2|) - 3) + 3) - 4) - 5 where -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 number of x-intercepts of the function f(x) = -2sin(3\u03c0(3(-2(-1|((3x - 2)/(1x + 1))| + 1)^2 - 1(-1|((3x - 2)/(1x + 1))| + 1) + 3)^2 - 4(-2(-1|((3x - 2)/(1x + 1))| + 1)^2 - 1(-1|((3x - 2)/(1x + 1))| + 1) + 3) - 1) + 3) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "822", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1e^(-1(1|(2(1(2|x - 1| - 3) + 5) - 3) - 3| - 3)) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0((-1(-4(5(-1x + 3)^2 + 5(-1x + 3))^2 + 4(5(-1x + 3)^2 + 5(-1x + 3))) - 1)/(-2(-4(5(-1x + 3)^2 + 5(-1x + 3))^2 + 4(5(-1x + 3)^2 + 5(-1x + 3))) + 3)) - 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(2|(-3|(2(-3x - 1) + 3) - 3| + 3) + 3| - 3) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(1|(2|(-4(-1sin(1\u03c0x) + 1)) - 2| - 3) - 1| - 3) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((2(3|(3(-1x^2 + 4x - 3)^2 - 1(-1x^2 + 4x - 3) - 5) + 2| - 1) + 1)/(1(3|(3(-1x^2 + 4x - 3)^2 - 1(-1x^2 + 4x - 3) - 5) + 2| - 1) + 2)) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(3(-2(-2|(-2x^2 - 3x + 3)| + 1)^2 - 5(-2|(-2x^2 - 3x + 3)| + 1) + 5)^2 - 5(-2(-2|(-2x^2 - 3x + 3)| + 1)^2 - 5(-2|(-2x^2 - 3x + 3)| + 1) + 5) - 4) + 2)/(2(3(-2(-2|(-2x^2 - 3x + 3)| + 1)^2 - 5(-2|(-2x^2 - 3x + 3)| + 1) + 5)^2 - 5(-2(-2|(-2x^2 - 3x + 3)| + 1)^2 - 5(-2|(-2x^2 - 3x + 3)| + 1) + 5) - 4) + 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2cos(2\u03c0(5((3((-2((-3x + 1)/(-3x + 4)) + 3)/(3((-3x + 1)/(-3x + 4)) + 2)) + 3)/(3((-2((-3x + 1)/(-3x + 4)) + 3)/(3((-3x + 1)/(-3x + 4)) + 2))))^2 - 1((3((-2((-3x + 1)/(-3x + 4)) + 3)/(3((-3x + 1)/(-3x + 4)) + 2)) + 3)/(3((-2((-3x + 1)/(-3x + 4)) + 3)/(3((-3x + 1)/(-3x + 4)) + 2)))) - 5) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "835", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|((-2(-1cos(2\u03c0(4((-1x + 2)/(2x + 1))^2 - 4) - 3) - 1))/(-3(-1cos(2\u03c0(4((-1x + 2)/(2x + 1))^2 - 4) - 3) - 1) - 1)) - 1| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "55", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3((-1(-5(4(-1|x - 2|) + 5)^2 - 4(4(-1|x - 2|) + 5)) - 3)/(1(-5(4(-1|x - 2|) + 5)^2 - 4(4(-1|x - 2|) + 5)) + 1)) + 3)/(-1((-1(-5(4(-1|x - 2|) + 5)^2 - 4(4(-1|x - 2|) + 5)) - 3)/(1(-5(4(-1|x - 2|) + 5)^2 - 4(4(-1|x - 2|) + 5)) + 1)) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2|(1|(-3sin(3\u03c0(-3|(2|x + 3| + 2) - 1| - 3) - 3) - 2)|) - 2| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "560", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-3sin(2\u03c0((-3((3(2x - 3) - 1)/(1(2x - 3) + 2)) - 3)/(3((3(2x - 3) - 1)/(1(2x - 3) + 2)) - 1)) - 1) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "32", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5((-3(-4(-1(-1sin(3\u03c0x - 1) - 1))^2 + 5(-1(-1sin(3\u03c0x - 1) - 1)) + 3) + 3)/(2(-4(-1(-1sin(3\u03c0x - 1) - 1))^2 + 5(-1(-1sin(3\u03c0x - 1) - 1)) + 3)))^2 + 1((-3(-4(-1(-1sin(3\u03c0x - 1) - 1))^2 + 5(-1(-1sin(3\u03c0x - 1) - 1)) + 3) + 3)/(2(-4(-1(-1sin(3\u03c0x - 1) - 1))^2 + 5(-1(-1sin(3\u03c0x - 1) - 1)) + 3))) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "150", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-3(-3|(-1(3|(-2cos(2\u03c0x)) - 2| - 3)^2 + 5(3|(-2cos(2\u03c0x)) - 2| - 3) - 4) + 3| + 1) - 3)/(2(-3|(-1(3|(-2cos(2\u03c0x)) - 2| - 3)^2 + 5(3|(-2cos(2\u03c0x)) - 2| - 3) - 4) + 3| + 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "128", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(4((-1(2(-5x^2 + 5x + 3)^2 + 3(-5x^2 + 5x + 3) - 4))/(-1(2(-5x^2 + 5x + 3)^2 + 3(-5x^2 + 5x + 3) - 4) + 2))^2 + 5((-1(2(-5x^2 + 5x + 3)^2 + 3(-5x^2 + 5x + 3) - 4))/(-1(2(-5x^2 + 5x + 3)^2 + 3(-5x^2 + 5x + 3) - 4) + 2)) - 4)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(2|(3cos(2\u03c0(2|((-1x - 3)/(3x - 2)) - 1| + 1) - 2) - 2)| - 2)^2 - 3(2|(3cos(2\u03c0(2|((-1x - 3)/(3x - 2)) - 1| + 1) - 2) - 2)| - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "122", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(5(2(-2(-1|x - 1|)^2 - 5(-1|x - 1|) - 2)) - 2)^2 - 1(5(2(-2(-1|x - 1|)^2 - 5(-1|x - 1|) - 2)) - 2) have 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 number of x-intercepts of the function f(x) = (-2(1|(1(-5(1sin(1\u03c0x + 3))^2 - 1(1sin(1\u03c0x + 3)) + 4)^2 + 2(-5(1sin(1\u03c0x + 3))^2 - 1(1sin(1\u03c0x + 3)) + 4) - 3) + 1| - 2) + 1)/(-3(1|(1(-5(1sin(1\u03c0x + 3))^2 - 1(1sin(1\u03c0x + 3)) + 4)^2 + 2(-5(1sin(1\u03c0x + 3))^2 - 1(1sin(1\u03c0x + 3)) + 4) - 3) + 1| - 2)) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(1|(3(-3|(3|x| - 2) + 2| + 2) + 3) - 2| - 2) + 1)/(2(1|(3(-3|(3|x| - 2) + 2| + 2) + 3) - 2| - 2) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(2(2|(-3(3sin(1\u03c0x - 3) + 1)^2 + 5) + 1| - 2) - 5) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(4(1|((-3(1x - 4) - 3)/(-1(1x - 4) + 2)) + 2| - 1)^2 - 5(1|((-3(1x - 4) - 3)/(-1(1x - 4) + 2)) + 2| - 1) - 5) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(2\u03c0(-4(-3(1(1x + 4) + 4) - 1)^2 + 4(-3(1(1x + 4) + 4) - 1) + 2)) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1511", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(2\u03c0(-2(3(-5(-4x^2 + 5x + 2)^2 - 2(-4x^2 + 5x + 2) - 3)^2 - 5(-5(-4x^2 + 5x + 2)^2 - 2(-4x^2 + 5x + 2) - 3) + 5) - 3) - 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "189", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(1cos(1\u03c0(1|((2(-5x) + 1)/(-1(-5x) + 2)) + 1| - 1) + 1) - 2) - 3)/(1(1cos(1\u03c0(1|((2(-5x) + 1)/(-1(-5x) + 2)) + 1| - 1) + 1) - 2) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "33", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2cos(3\u03c0(1(4(4((-2x + 3)/(1x - 2))^2 - 2((-2x + 3)/(1x - 2)) + 5)^2 + 1(4((-2x + 3)/(1x - 2))^2 - 2((-2x + 3)/(1x - 2)) + 5) - 5)^2 - 3(4(4((-2x + 3)/(1x - 2))^2 - 2((-2x + 3)/(1x - 2)) + 5)^2 + 1(4((-2x + 3)/(1x - 2))^2 - 2((-2x + 3)/(1x - 2)) + 5) - 5) + 1) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "38", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2((1(5(4(-2sin(3\u03c0x - 3) - 2) + 3) + 5))/(-1(5(4(-2sin(3\u03c0x - 3) - 2) + 3) + 5) - 2)) - 1)/(2((1(5(4(-2sin(3\u03c0x - 3) - 2) + 3) + 5))/(-1(5(4(-2sin(3\u03c0x - 3) - 2) + 3) + 5) - 2)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (1(2cos(1\u03c0(2|(-2|(1x - 3) - 1| + 1)|)) - 2))/(-3(2cos(1\u03c0(2|(-2|(1x - 3) - 1| + 1)|)) - 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "41", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(1cos(3\u03c0(3|(-1(1x - 3)^2 + 5(1x - 3) - 5) + 2|) + 2) - 2) - 3)/(-1(1cos(3\u03c0(3|(-1(1x - 3)^2 + 5(1x - 3) - 5) + 2|) + 2) - 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "884", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-2(-4(-1|(-3x - 3) - 2| + 2) - 4) - 1)^2 - 1(-2(-4(-1|(-3x - 3) - 2| + 2) - 4) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4((-3(3|(3(-1|x - 3|) + 5) + 1|) + 1)/(3(3|(3(-1|x - 3|) + 5) + 1|) - 2)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-3e^(2(-5(1(1|x + 2|)^2 + 4(1|x + 2|) - 4) + 3)) + 2)^2 + 3(-3e^(2(-5(1(1|x + 2|)^2 + 4(1|x + 2|) - 4) + 3)) + 2) - 4 where -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 number of x-intercepts of the function f(x) = (2((-3(3cos(2\u03c0(4(3|x - 2| - 3) + 5) - 3) - 3) + 1)/(-1(3cos(2\u03c0(4(3|x - 2| - 3) + 5) - 3) - 3) - 1)) + 2)/(2((-3(3cos(2\u03c0(4(3|x - 2| - 3) + 5) - 3) - 3) + 1)/(-1(3cos(2\u03c0(4(3|x - 2| - 3) + 5) - 3) - 3) - 1)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "229", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(-1(-1(3sin(1\u03c0(-4x^2 - 4x - 5) + 3) + 3)^2 + 2(3sin(1\u03c0(-4x^2 - 4x - 5) + 3) + 3) + 5)^2 - 2(-1(3sin(1\u03c0(-4x^2 - 4x - 5) + 3) + 3)^2 + 2(3sin(1\u03c0(-4x^2 - 4x - 5) + 3) + 3) + 5)) + 1| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "463", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1((2((3((3(1|x + 2| - 3) + 1)/(2(1|x + 2| - 3))))/(-2((3(1|x + 2| - 3) + 1)/(2(1|x + 2| - 3))) - 2)) + 3)/(2((3((3(1|x + 2| - 3) + 1)/(2(1|x + 2| - 3))))/(-2((3(1|x + 2| - 3) + 1)/(2(1|x + 2| - 3))) - 2)) - 1))^2 + 4((2((3((3(1|x + 2| - 3) + 1)/(2(1|x + 2| - 3))))/(-2((3(1|x + 2| - 3) + 1)/(2(1|x + 2| - 3))) - 2)) + 3)/(2((3((3(1|x + 2| - 3) + 1)/(2(1|x + 2| - 3))))/(-2((3(1|x + 2| - 3) + 1)/(2(1|x + 2| - 3))) - 2)) - 1)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(-2|((-1(2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) - 3) - 3)/(-1(2((1x + 3)/(-3x + 1))^2 + 1((1x + 3)/(-3x + 1)) - 3))) + 3| + 3) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1((-2(2sin(1\u03c0(5(-4x^2 - 4x - 4) + 5)) - 2) + 2)/(3(2sin(1\u03c0(5(-4x^2 - 4x - 4) + 5)) - 2) + 3)) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "798", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(-2(-1((2(2sin(3\u03c0x + 2) + 1) - 3)/(1(2sin(3\u03c0x + 2) + 1) - 3)) - 2)^2 + 5) + 1)/(-1(-2(-1((2(2sin(3\u03c0x + 2) + 1) - 3)/(1(2sin(3\u03c0x + 2) + 1) - 3)) - 2)^2 + 5) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "108", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(3\u03c0((2((-2((3(3x) - 2)/(-1(3x) - 2)) - 3)/(-3((3(3x) - 2)/(-1(3x) - 2)))) + 3)/(1((-2((3(3x) - 2)/(-1(3x) - 2)) - 3)/(-3((3(3x) - 2)/(-1(3x) - 2)))) + 3)) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(3\u03c0(-1(-3|(2|(2|x - 1| - 3) + 2| + 2) + 1| - 1)^2 - 3(-3|(2|(2|x - 1| - 3) + 2| + 2) + 1| - 1) - 2) + 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1300", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2((-3((3(3(1cos(2\u03c0x - 1) + 2)^2 - 1(1cos(2\u03c0x - 1) + 2) - 5) - 3)/(-1(3(1cos(2\u03c0x - 1) + 2)^2 - 1(1cos(2\u03c0x - 1) + 2) - 5) - 2)) + 3)/(-3((3(3(1cos(2\u03c0x - 1) + 2)^2 - 1(1cos(2\u03c0x - 1) + 2) - 5) - 3)/(-1(3(1cos(2\u03c0x - 1) + 2)^2 - 1(1cos(2\u03c0x - 1) + 2) - 5) - 2)) + 4)) + 1)/(1((-3((3(3(1cos(2\u03c0x - 1) + 2)^2 - 1(1cos(2\u03c0x - 1) + 2) - 5) - 3)/(-1(3(1cos(2\u03c0x - 1) + 2)^2 - 1(1cos(2\u03c0x - 1) + 2) - 5) - 2)) + 3)/(-3((3(3(1cos(2\u03c0x - 1) + 2)^2 - 1(1cos(2\u03c0x - 1) + 2) - 5) - 3)/(-1(3(1cos(2\u03c0x - 1) + 2)^2 - 1(1cos(2\u03c0x - 1) + 2) - 5) - 2)) + 4))) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(3\u03c0((-2(4(5((2x + 3)/(1x)) + 3) + 5) + 3)/(-3(4(5((2x + 3)/(1x)) + 3) + 5))) + 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-1(2|(-3(1(-1x)^2 - 2(-1x) - 3) + 5) + 1| - 3) - 1)/(2(2|(-3(1(-1x)^2 - 2(-1x) - 3) + 5) + 1| - 3)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3cos(1\u03c0(-1|(1|(3x^2 - 1x - 5) - 2|) + 2| + 1) + 1) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "272", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3|(-1(-1(-2(-3sin(2\u03c0x - 3) + 1) + 1)^2 - 5(-2(-3sin(2\u03c0x - 3) + 1) + 1) + 1)^2 - 4(-1(-2(-3sin(2\u03c0x - 3) + 1) + 1)^2 - 5(-2(-3sin(2\u03c0x - 3) + 1) + 1) + 1)) + 3| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "109", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(1(-1cos(1\u03c0(-4(1|x - 3| + 2)^2 - 4(1|x - 3| + 2)) + 2) - 3) + 2) - 3)/(2(1(-1cos(1\u03c0(-4(1|x - 3| + 2)^2 - 4(1|x - 3| + 2)) + 2) - 3) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1236", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2(-2cos(1\u03c0(-5(-1|(3|x - 3| + 1) - 3| - 1) - 4) - 1) + 1)^2 - 3(-2cos(1\u03c0(-5(-1|(3|x - 3| + 1) - 3| - 1) - 4) - 1) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "600", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(3cos(3\u03c0(-1(-1(1x^2 + 4)^2 + 4(1x^2 + 4) + 2) - 2) + 3) - 1) - 1)/(-1(3cos(3\u03c0(-1(-1(1x^2 + 4)^2 + 4(1x^2 + 4) + 2) - 2) + 3) - 1) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1317", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3e^(1(-4(3(-4(-1|x + 1| + 1) - 3)^2 - 2(-4(-1|x + 1| + 1) - 3) - 4)^2 + 2(3(-4(-1|x + 1| + 1) - 3)^2 - 2(-4(-1|x + 1| + 1) - 3) - 4) + 4)) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1|(2|(-5((2(-1x + 4) + 1)/(2(-1x + 4) + 2)) + 5)| - 3) - 3| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-5(-1|(3|(3x^2 + 5x)|)| + 3) - 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2cos(2\u03c0((2(1(-3(5x + 2)^2 + 5(5x + 2) - 2)))/(-2(1(-3(5x + 2)^2 + 5(5x + 2) - 2)) - 1)) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|(2cos(2\u03c0(-1|(-2|((-2x + 2)/(2x + 2)) - 3| - 2) - 3| + 1) + 3) - 1)| - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "135", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(-1|(5((3(-2|x - 1| + 2) - 3)/(-2(-2|x - 1| + 2) - 2))^2 - 2((3(-2|x - 1| + 2) - 3)/(-2(-2|x - 1| + 2) - 2)) - 4)| + 3) - 3)/(-1(-1|(5((3(-2|x - 1| + 2) - 3)/(-2(-2|x - 1| + 2) - 2))^2 - 2((3(-2|x - 1| + 2) - 3)/(-2(-2|x - 1| + 2) - 2)) - 4)| + 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0(2|(1(-1(-1x + 3) + 4) - 4) - 3| + 3) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-5(-5(-3|(-1|x + 3| + 1)| + 1)^2 - 2(-3|(-1|x + 3| + 1)| + 1)) - 2) - 2| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(5(-1(2sin(2\u03c0(-2x + 3) + 3))^2 - 2(2sin(2\u03c0(-2x + 3) + 3)) + 3))^2 + 3(5(-1(2sin(2\u03c0(-2x + 3) + 3))^2 - 2(2sin(2\u03c0(-2x + 3) + 3)) + 3)) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "77", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(1(3(1(2|x - 3| - 1) - 3) - 2)^2 + 5(3(1(2|x - 3| - 1) - 3) - 2) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(1|(-1(3|(1x^2 + 3x + 1) - 1| + 2)^2 + 1(3|(1x^2 + 3x + 1) - 1| + 2) - 4) + 1| + 3) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1031", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(5(-1(1|((-1x)/(1x + 1)) - 3| - 1)^2 - 4(1|((-1x)/(1x + 1)) - 3| - 1) + 3)^2 - 4) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-2((3(2sin(1\u03c0(-1x + 2) - 2)) - 2)/(-2(2sin(1\u03c0(-1x + 2) - 2)) - 1))^2 + 2((3(2sin(1\u03c0(-1x + 2) - 2)) - 2)/(-2(2sin(1\u03c0(-1x + 2) - 2)) - 1))) + 2)/(2(-2((3(2sin(1\u03c0(-1x + 2) - 2)) - 2)/(-2(2sin(1\u03c0(-1x + 2) - 2)) - 1))^2 + 2((3(2sin(1\u03c0(-1x + 2) - 2)) - 2)/(-2(2sin(1\u03c0(-1x + 2) - 2)) - 1))) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (3(2cos(3\u03c0(3|(1|(4x - 2) + 3| + 1)| - 2)) + 1))/(3(2cos(3\u03c0(3|(1|(4x - 2) + 3| + 1)| - 2)) + 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "604", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(1(-1|(1((-3x + 3)/(3x + 1))^2 - 3((-3x + 3)/(3x + 1)) - 5) - 1| + 3) + 4)^2 + 3(1(-1|(1((-3x + 3)/(3x + 1))^2 - 3((-3x + 3)/(3x + 1)) - 5) - 1| + 3) + 4) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -4(4(4(2(3x^2 - 1x - 3)^2 - 2(3x^2 - 1x - 3))^2 + 4(2(3x^2 - 1x - 3)^2 - 2(3x^2 - 1x - 3)) - 4) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3|(1|(-1|(-2|((1x)/(-3x + 4)) + 3| + 3) + 2| + 2)| - 3) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(3|((1(-3sin(2\u03c0(4x - 1) + 2) - 1) + 3)/(1(-3sin(2\u03c0(4x - 1) + 2) - 1) - 3)) + 3| - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(3|(-3(3cos(2\u03c0(-5x - 3) + 2) - 1)^2 - 2(3cos(2\u03c0(-5x - 3) + 2) - 1) + 2) - 1| - 2) + 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "188", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-3cos(3\u03c0(-2|(4(-1|x + 3| - 2)^2 + 3(-1|x + 3| - 2) + 1) - 1| - 3) - 3) - 2) - 1| = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1228", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-4(-1(-3(2x - 5) + 5)^2 + 4(-3(2x - 5) + 5) + 4)^2 - 1(-1(-3(2x - 5) + 5)^2 + 4(-3(2x - 5) + 5) + 4) + 5)^2 - 5(-4(-1(-3(2x - 5) + 5)^2 + 4(-3(2x - 5) + 5) + 4)^2 - 1(-1(-3(2x - 5) + 5)^2 + 4(-3(2x - 5) + 5) + 4) + 5) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(-2|(-1((1(2x^2 - 2x - 3) - 2)/(-1(2x^2 - 2x - 3) - 1))^2 - 1((1(2x^2 - 2x - 3) - 2)/(-1(2x^2 - 2x - 3) - 1)) + 4) + 2| - 2)^2 + 4(-2|(-1((1(2x^2 - 2x - 3) - 2)/(-1(2x^2 - 2x - 3) - 1))^2 - 1((1(2x^2 - 2x - 3) - 2)/(-1(2x^2 - 2x - 3) - 1)) + 4) + 2| - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(3(1|(2cos(1\u03c0(1x^2 - 1x - 2) + 2) + 2) - 1| - 2)^2 + 3(1|(2cos(1\u03c0(1x^2 - 1x - 2) + 2) + 2) - 1| - 2) - 2)^2 + 2(3(1|(2cos(1\u03c0(1x^2 - 1x - 2) + 2) + 2) - 1| - 2)^2 + 3(1|(2cos(1\u03c0(1x^2 - 1x - 2) + 2) + 2) - 1| - 2) - 2) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "578", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(-2|(-2e^(2((-1(-3|x| - 1) - 3)/(2(-3|x| - 1)))) + 1)| + 3) - 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1sin(2\u03c0(2|(-3(-1(-2|x - 2|)^2 + 2(-2|x - 2|) + 2)^2 + 4(-1(-2|x - 2|)^2 + 2(-2|x - 2|) + 2) + 5) + 2| - 1) - 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1106", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(5(5(-2|(-3x^2 - 3) + 3| - 3)^2 - 4(-2|(-3x^2 - 3) + 3| - 3) + 3)^2 - 4(5(-2|(-3x^2 - 3) + 3| - 3)^2 - 4(-2|(-3x^2 - 3) + 3| - 3) + 3) - 3)) - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-2(1(4(-1|x| + 2)^2 - 3(-1|x| + 2) + 1)^2 - 3(4(-1|x| + 2)^2 - 3(-1|x| + 2) + 1) + 1) + 4) + 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(-2|(-2(-1((-3x - 1)/(1x)) - 3) - 4) - 3|) - 1) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "101", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1|(-5(2|(-4((-3x - 2)/(3x))) - 2| - 3)^2 + 2(2|(-4((-3x - 2)/(3x))) - 2| - 3) - 1) - 1| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3\u03c0((-3(2(1(3x^2 + 5x + 1) - 2) - 5) - 3)/(-2(2(1(3x^2 + 5x + 1) - 2) - 5))) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(5(5(3(5x)^2 - 2(5x) - 1) - 1) - 4)^2 - 2(5(5(3(5x)^2 - 2(5x) - 1) - 1) - 4) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-2cos(2\u03c0(-2(-3|(-1|x - 1| + 2) - 2| + 1)^2 - 2(-3|(-1|x - 1| + 2) - 2| + 1) - 2)) - 2) + 2)/(2(-2cos(2\u03c0(-2(-3|(-1|x - 1| + 2) - 2| + 1)^2 - 2(-3|(-1|x - 1| + 2) - 2| + 1) - 2)) - 2) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "766", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1sin(1\u03c0(1(5(-1|x - 3| + 2) - 1)) - 2) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "51", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(3cos(3\u03c0(-2|((-3(-5x^2 - 1x + 2) - 2)/(-2(-5x^2 - 1x + 2) - 2)) - 2| - 3) + 1) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "36", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-2(-1(-4(3(-1x - 1) - 2)^2 + 2(3(-1x - 1) - 2) + 5)^2 + 4(-4(3(-1x - 1) - 2)^2 + 2(3(-1x - 1) - 2) + 5) - 2) + 3)/(-3(-1(-4(3(-1x - 1) - 2)^2 + 2(3(-1x - 1) - 2) + 5)^2 + 4(-4(3(-1x - 1) - 2)^2 + 2(3(-1x - 1) - 2) + 5) - 2)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-3(-4((-3(3sin(2\u03c0x)) + 2)/(3(3sin(2\u03c0x))))^2 + 5((-3(3sin(2\u03c0x)) + 2)/(3(3sin(2\u03c0x)))) + 5)))/(-1(-3(-4((-3(3sin(2\u03c0x)) + 2)/(3(3sin(2\u03c0x))))^2 + 5((-3(3sin(2\u03c0x)) + 2)/(3(3sin(2\u03c0x)))) + 5)) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(2\u03c0(3|(2|((2(4x^2 - 5x - 2) - 3)/(2(4x^2 - 5x - 2) - 1)) - 1| - 3) + 2| + 3) + 2) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2((-2(1((-1(-5x^2 + 4x + 3) - 1)/(-1(-5x^2 + 4x + 3) - 3))^2 + 5((-1(-5x^2 + 4x + 3) - 1)/(-1(-5x^2 + 4x + 3) - 3)) + 4) + 3)/(-1(1((-1(-5x^2 + 4x + 3) - 1)/(-1(-5x^2 + 4x + 3) - 3))^2 + 5((-1(-5x^2 + 4x + 3) - 1)/(-1(-5x^2 + 4x + 3) - 3)) + 4) + 2))^2 + 1((-2(1((-1(-5x^2 + 4x + 3) - 1)/(-1(-5x^2 + 4x + 3) - 3))^2 + 5((-1(-5x^2 + 4x + 3) - 1)/(-1(-5x^2 + 4x + 3) - 3)) + 4) + 3)/(-1(1((-1(-5x^2 + 4x + 3) - 1)/(-1(-5x^2 + 4x + 3) - 3))^2 + 5((-1(-5x^2 + 4x + 3) - 1)/(-1(-5x^2 + 4x + 3) - 3)) + 4) + 2)) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2((1(2(-2sin(2\u03c0(1x^2 + 5x - 3) - 1) - 1)^2 - 1(-2sin(2\u03c0(1x^2 + 5x - 3) - 1) - 1) - 4) - 1)/(2(2(-2sin(2\u03c0(1x^2 + 5x - 3) - 1) - 1)^2 - 1(-2sin(2\u03c0(1x^2 + 5x - 3) - 1) - 1) - 4) - 1)) + 3)/(-3((1(2(-2sin(2\u03c0(1x^2 + 5x - 3) - 1) - 1)^2 - 1(-2sin(2\u03c0(1x^2 + 5x - 3) - 1) - 1) - 4) - 1)/(2(2(-2sin(2\u03c0(1x^2 + 5x - 3) - 1) - 1)^2 - 1(-2sin(2\u03c0(1x^2 + 5x - 3) - 1) - 1) - 4) - 1)) + 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "164", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(1\u03c0(2|(-2|(-1|((3x + 3)/(2x)) - 3| + 2) - 2| - 1) - 1|) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-5((-3(3(-2|x + 3| + 1) + 4))/(1(3(-2|x + 3| + 1) + 4) + 2))^2 + 5((-3(3(-2|x + 3| + 1) + 4))/(1(3(-2|x + 3| + 1) + 4) + 2))) - 1)/(-2(-5((-3(3(-2|x + 3| + 1) + 4))/(1(3(-2|x + 3| + 1) + 4) + 2))^2 + 5((-3(3(-2|x + 3| + 1) + 4))/(1(3(-2|x + 3| + 1) + 4) + 2))) - 1) have 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 number of x-intercepts of the function f(x) = 2(-5(-3cos(3\u03c0((-2(5x) + 1)/(-3(5x) - 1)) + 1) + 3) + 2)^2 + 3(-5(-3cos(3\u03c0((-2(5x) + 1)/(-3(5x) - 1)) + 1) + 3) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "18", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(4(-4(3|(-3x^2 - 4x + 2) - 1| - 2) + 5)^2 + 5(-4(3|(-3x^2 - 4x + 2) - 1| - 2) + 5) - 3)^2 + 4(4(-4(3|(-3x^2 - 4x + 2) - 1| - 2) + 5)^2 + 5(-4(3|(-3x^2 - 4x + 2) - 1| - 2) + 5) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3((-1(2((-3(2x^2 + 2x - 4) - 1)/(2(2x^2 + 2x - 4) - 1))^2 - 5) + 3)/(-2(2((-3(2x^2 + 2x - 4) - 1)/(2(2x^2 + 2x - 4) - 1))^2 - 5) + 3)) - 2)/(-2((-1(2((-3(2x^2 + 2x - 4) - 1)/(2(2x^2 + 2x - 4) - 1))^2 - 5) + 3)/(-2(2((-3(2x^2 + 2x - 4) - 1)/(2(2x^2 + 2x - 4) - 1))^2 - 5) + 3)) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2cos(1\u03c0(3(-1(2|(4x^2 + 5x + 3) + 3| + 2) + 2) - 4) + 2) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1449", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(1(-2e^(-1(5(1|x + 3| - 1)^2 - 1(1|x + 3| - 1) - 2)) + 2)^2 - 5(-2e^(-1(5(1|x + 3| - 1)^2 - 1(1|x + 3| - 1) - 2)) + 2) - 3))/(2(1(-2e^(-1(5(1|x + 3| - 1)^2 - 1(1|x + 3| - 1) - 2)) + 2)^2 - 5(-2e^(-1(5(1|x + 3| - 1)^2 - 1(1|x + 3| - 1) - 2)) + 2) - 3) - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(-2|(1|(2|(-5x^2 + 2x) + 1| - 1)| + 2) - 3| + 3)^2 - 3(-2|(1|(2|(-5x^2 + 2x) + 1| - 1)| + 2) - 3| + 3) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-4((2(1(1x^2 - 4x - 1)^2 + 4(1x^2 - 4x - 1) - 3) + 3)/(-3(1(1x^2 - 4x - 1)^2 + 4(1x^2 - 4x - 1) - 3) + 2)) + 4) + 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1|(4((3(1sin(2\u03c0(2|x + 3|))) + 3)/(3(1sin(2\u03c0(2|x + 3|))) - 2))^2 - 5((3(1sin(2\u03c0(2|x + 3|))) + 3)/(3(1sin(2\u03c0(2|x + 3|))) - 2)) - 3) - 1| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2sin(3\u03c0(1(-3|(-5(-3|x + 3| - 1)^2 - 3(-3|x + 3| - 1) + 1) - 3| + 3)^2 - 1(-3|(-5(-3|x + 3| - 1)^2 - 3(-3|x + 3| - 1) + 1) - 3| + 3) - 3) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3((2(2sin(3\u03c0(3|((1x + 2)/(-2x + 3)) - 1| - 3) - 1) + 1) - 1)/(-2(2sin(3\u03c0(3|((1x + 2)/(-2x + 3)) - 1| - 3) - 1) + 1))) - 1)/(2((2(2sin(3\u03c0(3|((1x + 2)/(-2x + 3)) - 1| - 3) - 1) + 1) - 1)/(-2(2sin(3\u03c0(3|((1x + 2)/(-2x + 3)) - 1| - 3) - 1) + 1))) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "65", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(3sin(3\u03c0(2(-2|(1|x - 1| + 3) + 3| + 2) + 2) - 1)) - 1)/(-1(3sin(3\u03c0(2(-2|(1|x - 1| + 3) + 3| + 2) + 2) - 1)) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-3|(1(2(1|x - 2| + 1) - 5) - 1) + 3| + 1) + 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(3\u03c0(2|(5((-2((2x + 2)/(-1x + 3)) - 1)/(1((2x + 2)/(-1x + 3)) - 2)) - 2) - 3| - 1) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "277", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(2(-2|(-2(-3|x + 1| - 1)^2 + 1(-3|x + 1| - 1) + 2) + 3| + 2)^2 - 1(-2|(-2(-3|x + 1| - 1)^2 + 1(-3|x + 1| - 1) + 2) + 3| + 2) - 3)^2 - 4(2(-2|(-2(-3|x + 1| - 1)^2 + 1(-3|x + 1| - 1) + 2) + 3| + 2)^2 - 1(-2|(-2(-3|x + 1| - 1)^2 + 1(-3|x + 1| - 1) + 2) + 3| + 2) - 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "14", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(1|(-1|(1e^(1(1x^2 - 5x + 4)) - 3) - 3| + 1) + 1| - 1) - 2 have 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 number of x-intercepts of the function f(x) = 1(2|(-3(3cos(2\u03c0((1x - 3)/(-1x - 1)) - 3) - 2) + 2) + 1| - 3)^2 + 1(2|(-3(3cos(2\u03c0((1x - 3)/(-1x - 1)) - 3) - 2) + 2) + 1| - 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "71", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1((-2(3(-1(3cos(3\u03c0x + 2) + 2) - 2) + 4) - 1)/(2(3(-1(3cos(3\u03c0x + 2) + 2) - 2) + 4) + 2))^2 + 4((-2(3(-1(3cos(3\u03c0x + 2) + 2) - 2) + 4) - 1)/(2(3(-1(3cos(3\u03c0x + 2) + 2) - 2) + 4) + 2)) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "44", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3cos(3\u03c0(1(3((-2(5x^2 + 1x - 3) - 1)/(-1(5x^2 + 1x - 3) - 2))^2)^2 + 4(3((-2(5x^2 + 1x - 3) - 1)/(-1(5x^2 + 1x - 3) - 2))^2) + 4) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "475", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(5(1cos(2\u03c0(-1|(4x^2 - 2x + 1) - 3|) - 1) + 1)^2 - 1(1cos(2\u03c0(-1|(4x^2 - 2x + 1) - 3|) - 1) + 1) + 1) + 2)/(1(5(1cos(2\u03c0(-1|(4x^2 - 2x + 1) - 3|) - 1) + 1)^2 - 1(1cos(2\u03c0(-1|(4x^2 - 2x + 1) - 3|) - 1) + 1) + 1) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1278", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2(1(5(-3|((-1x - 2)/(-2x - 2)) - 1| + 1) + 1) - 3)^2 - 3(1(5(-3|((-1x - 2)/(-2x - 2)) - 1| + 1) + 1) - 3) have 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 number of x-intercepts of the function f(x) = -2sin(3\u03c0((3(1((3(-1x^2 - 1x + 3) + 3)/(-3(-1x^2 - 1x + 3))) - 3) - 1)/(3(1((3(-1x^2 - 1x + 3) + 3)/(-3(-1x^2 - 1x + 3))) - 3) + 2)) - 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-2|((2((3(-4x^2 + 5x) + 1)/(3(-4x^2 + 5x) - 2)))/(-2((3(-4x^2 + 5x) + 1)/(3(-4x^2 + 5x) - 2)) - 3)) - 2| + 3) - 2)/(1(-2|((2((3(-4x^2 + 5x) + 1)/(3(-4x^2 + 5x) - 2)))/(-2((3(-4x^2 + 5x) + 1)/(3(-4x^2 + 5x) - 2)) - 3)) - 2| + 3) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(5(3(3(2|x| - 3) + 3) - 5) + 5)^2 + 5(5(3(3(2|x| - 3) + 3) - 5) + 5) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1(-3cos(1\u03c0(-2|(5(1|x - 2| - 2)^2 - 3(1|x - 2| - 2) + 1) - 3| + 2) - 3)) + 3)/(3(-3cos(1\u03c0(-2|(5(1|x - 2| - 2)^2 - 3(1|x - 2| - 2) + 1) - 3| + 2) - 3)) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "667", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(1\u03c0(-1(-2|((-3(-1|x - 2| - 3) - 1)/(-3(-1|x - 2| - 3) + 4)) - 2| - 3)^2 - 5(-2|((-3(-1|x - 2| - 3) - 1)/(-3(-1|x - 2| - 3) + 4)) - 2| - 3) + 3) + 3) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-4((-3(1|(-1|x + 1| - 1) + 2| - 3) + 2)/(1(1|(-1|x + 1| - 1) + 2| - 3)))^2 - 3((-3(1|(-1|x + 1| - 1) + 2| - 3) + 2)/(1(1|(-1|x + 1| - 1) + 2| - 3))) - 1) - 1)/(-3(-4((-3(1|(-1|x + 1| - 1) + 2| - 3) + 2)/(1(1|(-1|x + 1| - 1) + 2| - 3)))^2 - 3((-3(1|(-1|x + 1| - 1) + 2| - 3) + 2)/(1(1|(-1|x + 1| - 1) + 2| - 3))) - 1)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3sin(2\u03c0(2(1(-4(-3x + 3)^2 + 3(-3x + 3) + 3) - 5) - 2) - 2) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1197", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(2((2(2|(-3|x| + 3) + 1| - 2) + 1)/(-2(2|(-3|x| + 3) + 1| - 2) + 1)) - 3))/(3(2((2(2|(-3|x| + 3) + 1| - 2) + 1)/(-2(2|(-3|x| + 3) + 1| - 2) + 1)) - 3) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(-3(-1|(1(1x^2 - 4x) + 2)| - 1)^2 - 3(-1|(1(1x^2 - 4x) + 2)| - 1) + 2) - 3)/(-3(-3(-1|(1(1x^2 - 4x) + 2)| - 1)^2 - 3(-1|(1(1x^2 - 4x) + 2)| - 1) + 2)) where -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 number of x-intercepts of the function f(x) = -5(5(5((1(-2x - 1) + 1)/(-2(-2x - 1) + 3))^2 - 2((1(-2x - 1) + 1)/(-2(-2x - 1) + 3)) - 5)^2 + 3(5((1(-2x - 1) + 1)/(-2(-2x - 1) + 3))^2 - 2((1(-2x - 1) + 1)/(-2(-2x - 1) + 3)) - 5) - 4)^2 + 2(5(5((1(-2x - 1) + 1)/(-2(-2x - 1) + 3))^2 - 2((1(-2x - 1) + 1)/(-2(-2x - 1) + 3)) - 5)^2 + 3(5((1(-2x - 1) + 1)/(-2(-2x - 1) + 3))^2 - 2((1(-2x - 1) + 1)/(-2(-2x - 1) + 3)) - 5) - 4) + 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2sin(2\u03c0(5(-2(1|(-1|x + 1| - 3) - 3| + 3)^2 - 5(1|(-1|x + 1| - 3) - 3| + 3) - 3)^2 - 5(-2(1|(-1|x + 1| - 3) - 3| + 3)^2 - 5(1|(-1|x + 1| - 3) - 3| + 3) - 3) - 5) + 2) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "96", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-5(1sin(2\u03c0(-2|(-3x^2 - 3x - 1) + 1| - 2) + 1) - 1)^2 - 4(1sin(2\u03c0(-2|(-3x^2 - 3x - 1) + 1| - 2) + 1) - 1) - 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1613", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0(-3(-1(1((1x - 2)/(1x + 3)) - 5) + 1) - 5)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "202", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(3sin(3\u03c0(2|(-2(-2x - 1) + 4)|) - 2) + 2) + 2| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-2((3(1cos(3\u03c0(-3x + 5) - 1) - 1))/(-1(1cos(3\u03c0(-3x + 5) - 1) - 1) - 1))^2 + 3((3(1cos(3\u03c0(-3x + 5) - 1) - 1))/(-1(1cos(3\u03c0(-3x + 5) - 1) - 1) - 1)) - 2) - 3)/(1(-2((3(1cos(3\u03c0(-3x + 5) - 1) - 1))/(-1(1cos(3\u03c0(-3x + 5) - 1) - 1) - 1))^2 + 3((3(1cos(3\u03c0(-3x + 5) - 1) - 1))/(-1(1cos(3\u03c0(-3x + 5) - 1) - 1) - 1)) - 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "81", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2|(-3sin(1\u03c0((1(-3(-1x - 2)^2 + 4(-1x - 2) + 2) - 2)/(2(-3(-1x - 2)^2 + 4(-1x - 2) + 2) + 3)) + 3) - 2) + 3| + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "48", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -4(-1(-2(2|((1x)/(-2x + 3))|) + 1) - 3)^2 + 2(-1(-2(2|((1x)/(-2x + 3))|) + 1) - 3) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-1|((-2(-2(2cos(2\u03c0x + 1) - 3) - 1) + 3)/(-1(-2(2cos(2\u03c0x + 1) - 3) - 1) + 2))| + 3) - 2| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "58", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(2(-1((-3(2x^2 + 3x + 1) - 2)/(-3(2x^2 + 3x + 1) + 4))^2 + 4)^2 + 2(-1((-3(2x^2 + 3x + 1) - 2)/(-3(2x^2 + 3x + 1) + 4))^2 + 4) + 1) - 3)/(-1(2(-1((-3(2x^2 + 3x + 1) - 2)/(-3(2x^2 + 3x + 1) + 4))^2 + 4)^2 + 2(-1((-3(2x^2 + 3x + 1) - 2)/(-3(2x^2 + 3x + 1) + 4))^2 + 4) + 1) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3((3(1(-3cos(1\u03c0(4x + 5) - 1) + 2)) + 3)/(-2(1(-3cos(1\u03c0(4x + 5) - 1) + 2)) + 1)) - 2)/(-2((3(1(-3cos(1\u03c0(4x + 5) - 1) + 2)) + 3)/(-2(1(-3cos(1\u03c0(4x + 5) - 1) + 2)) + 1)) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2sin(2\u03c0(-3(3(-2|(1x^2 + 2x + 2) - 3|)) + 5) + 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1101", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0((-1((-2(5(2x - 2)) - 2)/(1(5(2x - 2)))) - 3)/(-1((-2(5(2x - 2)) - 2)/(1(5(2x - 2)))) - 1))) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((1(-2(-5(-2|x + 2| + 3)^2 + 3)) + 3)/(-1(-2(-5(-2|x + 2| + 3)^2 + 3)) + 2)) + 3 have 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 number of x-intercepts of the function f(x) = (2(-3|(1((-2(5x^2 - 3) + 3)/(1(5x^2 - 3) + 2))^2 - 3((-2(5x^2 - 3) + 3)/(1(5x^2 - 3) + 2))) - 3| + 3) + 2)/(-3(-3|(1((-2(5x^2 - 3) + 3)/(1(5x^2 - 3) + 2))^2 - 3((-2(5x^2 - 3) + 3)/(1(5x^2 - 3) + 2))) - 3| + 3) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1(-1((-2(4(2|x + 2| - 2)^2 + 2(2|x + 2| - 2) - 1) - 1)/(3(4(2|x + 2| - 2)^2 + 2(2|x + 2| - 2) - 1)))^2 - 3((-2(4(2|x + 2| - 2)^2 + 2(2|x + 2| - 2) - 1) - 1)/(3(4(2|x + 2| - 2)^2 + 2(2|x + 2| - 2) - 1))) + 5)^2 + 4(-1((-2(4(2|x + 2| - 2)^2 + 2(2|x + 2| - 2) - 1) - 1)/(3(4(2|x + 2| - 2)^2 + 2(2|x + 2| - 2) - 1)))^2 - 3((-2(4(2|x + 2| - 2)^2 + 2(2|x + 2| - 2) - 1) - 1)/(3(4(2|x + 2| - 2)^2 + 2(2|x + 2| - 2) - 1))) + 5) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "15", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(2\u03c0(4((-3(-1(5x - 3) - 5) + 2)/(-2(-1(5x - 3) - 5) + 3))^2 + 3((-3(-1(5x - 3) - 5) + 2)/(-2(-1(5x - 3) - 5) + 3)) + 4) - 2) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(2|(-2(3(-3|x - 1| - 1) + 4)^2 + 5(3(-3|x - 1| - 1) + 4) - 2) + 2|) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-2(1|((1(3sin(2\u03c0(-2x + 1) - 3) + 3))/(-1(3sin(2\u03c0(-2x + 1) - 3) + 3) + 3)) - 3| - 2) + 2)/(-2(1|((1(3sin(2\u03c0(-2x + 1) - 3) + 3))/(-1(3sin(2\u03c0(-2x + 1) - 3) + 3) + 3)) - 3| - 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-1(-4(-2cos(2\u03c0(3(-2|x + 2| + 3) - 4)) - 2)^2 + 2(-2cos(2\u03c0(3(-2|x + 2| + 3) - 4)) - 2) + 2) + 2)/(3(-4(-2cos(2\u03c0(3(-2|x + 2| + 3) - 4)) - 2)^2 + 2(-2cos(2\u03c0(3(-2|x + 2| + 3) - 4)) - 2) + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(3|((-1(2(3x^2 + 5x + 3) - 3) - 2)/(1(2(3x^2 + 5x + 3) - 3) + 1)) + 3| - 1) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2((1(-1sin(3\u03c0(-2(1|x + 1| - 3) - 2) + 2)) + 2)/(2(-1sin(3\u03c0(-2(1|x + 1| - 3) - 2) + 2)) + 1))^2 - 2((1(-1sin(3\u03c0(-2(1|x + 1| - 3) - 2) + 2)) + 2)/(2(-1sin(3\u03c0(-2(1|x + 1| - 3) - 2) + 2)) + 1)) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(2sin(1\u03c0(-2(3|(5x - 1)| + 3) + 1) - 2) + 2)^2 - 4(2sin(1\u03c0(-2(3|(5x - 1)| + 3) + 1) - 2) + 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "290", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3|(1e^(-1(-4((1(-4x^2 + 5x + 5) - 3)/(1(-4x^2 + 5x + 5)))^2 - 3((1(-4x^2 + 5x + 5) - 3)/(1(-4x^2 + 5x + 5))) - 1)) - 3) - 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3\u03c0(-2|(2(1|(1|x + 2| - 1)| - 3) - 4) + 1| + 3) - 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(-4(1|(-2cos(2\u03c0(-3x - 4))) - 3| + 1) + 3) + 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "59", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(-3|(-4(-2|(-3x + 1) + 2|)^2 + 3(-2|(-3x + 1) + 2|) + 4) + 2| - 1) - 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(1cos(1\u03c0(-3(-2(-3x^2 + 4x + 5)^2 + 1(-3x^2 + 4x + 5) - 2) - 3) + 2) + 2) + 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "786", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2((-3(3sin(2\u03c0(-4(3|x - 3| - 3)^2 - 1(3|x - 3| - 3) + 1) - 3) - 1) - 3)/(2(3sin(2\u03c0(-4(3|x - 3| - 3)^2 - 1(3|x - 3| - 3) + 1) - 3) - 1) + 1)) + 1)/(1((-3(3sin(2\u03c0(-4(3|x - 3| - 3)^2 - 1(3|x - 3| - 3) + 1) - 3) - 1) - 3)/(2(3sin(2\u03c0(-4(3|x - 3| - 3)^2 - 1(3|x - 3| - 3) + 1) - 3) - 1) + 1)) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "495", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(5(-4((2(2cos(1\u03c0x - 3) + 1) + 2)/(1(2cos(1\u03c0x - 3) + 1) - 3))^2 - 5((2(2cos(1\u03c0x - 3) + 1) + 2)/(1(2cos(1\u03c0x - 3) + 1) - 3)) + 2) + 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5((-2(2cos(3\u03c0(-1|(-1|x + 2| - 2)| - 2)) - 3) - 2)/(1(2cos(3\u03c0(-1|(-1|x + 2| - 2)| - 2)) - 3))) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(3(-3|(-2cos(3\u03c0(-2|x + 3| + 3) - 2) + 2) - 1| - 1) + 2) + 2| - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "240", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3((-3(-2(-3|(1x^2 + 4x - 1) - 3| - 1)^2 - 4(-3|(1x^2 + 4x - 1) - 3| - 1) - 1) - 3)/(-2(-2(-3|(1x^2 + 4x - 1) - 3| - 1)^2 - 4(-3|(1x^2 + 4x - 1) - 3| - 1) - 1) + 1)) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5((-2(2(-3(3cos(1\u03c0x - 2) + 3)^2 - 4(3cos(1\u03c0x - 2) + 3) + 3) - 5) + 1)/(-1(2(-3(3cos(1\u03c0x - 2) + 3)^2 - 4(3cos(1\u03c0x - 2) + 3) + 3) - 5) + 2))^2 + 5((-2(2(-3(3cos(1\u03c0x - 2) + 3)^2 - 4(3cos(1\u03c0x - 2) + 3) + 3) - 5) + 1)/(-1(2(-3(3cos(1\u03c0x - 2) + 3)^2 - 4(3cos(1\u03c0x - 2) + 3) + 3) - 5) + 2)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 5(-2((-3((-3(3|x + 3| - 3))/(-1(3|x + 3| - 3) + 2)) + 3)/(-2((-3(3|x + 3| - 3))/(-1(3|x + 3| - 3) + 2)) + 3))^2 - 3((-3((-3(3|x + 3| - 3))/(-1(3|x + 3| - 3) + 2)) + 3)/(-2((-3(3|x + 3| - 3))/(-1(3|x + 3| - 3) + 2)) + 3))) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2((1(3(2(3|x - 1| + 1)^2 - 3(3|x - 1| + 1) - 1) - 4) + 2)/(-2(3(2(3|x - 1| + 1)^2 - 3(3|x - 1| + 1) - 1) - 4)))^2 - 2((1(3(2(3|x - 1| + 1)^2 - 3(3|x - 1| + 1) - 1) - 4) + 2)/(-2(3(2(3|x - 1| + 1)^2 - 3(3|x - 1| + 1) - 1) - 4))) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(1cos(3\u03c0(-3(-3((-2x - 3)/(2x + 2))^2 + 5((-2x - 3)/(2x + 2)) + 3) - 5) + 1) - 1) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "204", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1((1(-5(-2cos(3\u03c0(-1|x + 2| - 1) - 2) - 1) - 5) + 2)/(-1(-5(-2cos(3\u03c0(-1|x + 2| - 1) - 2) - 1) - 5) - 3)) - 3)/(-3((1(-5(-2cos(3\u03c0(-1|x + 2| - 1) - 2) - 1) - 5) + 2)/(-1(-5(-2cos(3\u03c0(-1|x + 2| - 1) - 2) - 1) - 5) - 3)) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3((3(-5(-4(-2cos(1\u03c0x) + 1)^2 + 2(-2cos(1\u03c0x) + 1) + 5) - 2) + 3)/(-2(-5(-4(-2cos(1\u03c0x) + 1)^2 + 2(-2cos(1\u03c0x) + 1) + 5) - 2) - 1)) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1sin(1\u03c0(1(-5(5(-3|x + 1| + 1)) + 2) - 4) + 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "712", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-1(2sin(1\u03c0(1|(2x^2 + 4x - 2) - 1| + 3) + 2))^2 + 1(2sin(1\u03c0(1|(2x^2 + 4x - 2) - 1| + 3) + 2)) + 4)^2 + 5(-1(2sin(1\u03c0(1|(2x^2 + 4x - 2) - 1| + 3) + 2))^2 + 1(2sin(1\u03c0(1|(2x^2 + 4x - 2) - 1| + 3) + 2)) + 4) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "402", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-3cos(2\u03c0(-4((-3(4x^2 + 2x) - 3)/(-2(4x^2 + 2x) + 1))^2 - 1((-3(4x^2 + 2x) - 3)/(-2(4x^2 + 2x) + 1)) + 5) - 2) + 1) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "185", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3sin(1\u03c0((-2((-3(-4((1x + 3)/(-1x - 2)) + 5) - 3)/(2(-4((1x + 3)/(-1x - 2)) + 5))) - 1)/(1((-3(-4((1x + 3)/(-1x - 2)) + 5) - 3)/(2(-4((1x + 3)/(-1x - 2)) + 5))) - 3)) - 2) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (3(-5(-1|(-4(-1x + 4)^2 + 3(-1x + 4) - 1) + 3| + 1) - 5) - 2)/(-1(-5(-1|(-4(-1x + 4)^2 + 3(-1x + 4) - 1) + 3| + 1) - 5) + 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(1sin(3\u03c0(-4((-3(2|x + 1| + 3) - 3)/(1(2|x + 1| + 3) + 3))^2 + 2((-3(2|x + 1| + 3) - 3)/(1(2|x + 1| + 3) + 3)) + 2) + 2)) - 1)/(-3(1sin(3\u03c0(-4((-3(2|x + 1| + 3) - 3)/(1(2|x + 1| + 3) + 3))^2 + 2((-3(2|x + 1| + 3) - 3)/(1(2|x + 1| + 3) + 3)) + 2) + 2)) + 4) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "49", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -1|(-4((3(-5((-2x - 1)/(3x + 3))^2 - 4((-2x - 1)/(3x + 3)) + 2))/(-1(-5((-2x - 1)/(3x + 3))^2 - 4((-2x - 1)/(3x + 3)) + 2) + 2))^2 + 2((3(-5((-2x - 1)/(3x + 3))^2 - 4((-2x - 1)/(3x + 3)) + 2))/(-1(-5((-2x - 1)/(3x + 3))^2 - 4((-2x - 1)/(3x + 3)) + 2) + 2)) + 5) - 3| + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1((-2(5(-1sin(2\u03c0(2|x + 1| + 2) - 3))^2 - 5(-1sin(2\u03c0(2|x + 1| + 2) - 3)) + 1) + 2)/(-1(5(-1sin(2\u03c0(2|x + 1| + 2) - 3))^2 - 5(-1sin(2\u03c0(2|x + 1| + 2) - 3)) + 1))))/(-1((-2(5(-1sin(2\u03c0(2|x + 1| + 2) - 3))^2 - 5(-1sin(2\u03c0(2|x + 1| + 2) - 3)) + 1) + 2)/(-1(5(-1sin(2\u03c0(2|x + 1| + 2) - 3))^2 - 5(-1sin(2\u03c0(2|x + 1| + 2) - 3)) + 1))) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(2sin(3\u03c0(3|(3|(2x) - 1| + 3) + 1| - 3) + 2) - 3) - 1)/(-1(2sin(3\u03c0(3|(3|(2x) - 1| + 3) + 1| - 3) + 2) - 3) + 3) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "501", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-3(-3|(3cos(2\u03c0(4(-2|x + 2| + 3) - 4) - 2) + 2) + 1| + 3))/(1(-3|(3cos(2\u03c0(4(-2|x + 2| + 3) - 4) - 2) + 2) + 1| + 3) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "320", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 4(2sin(3\u03c0(-4(-5(-3x^2 + 3x + 5) + 4)^2 + 4(-5(-3x^2 + 3x + 5) + 4) - 4) - 3) - 3)^2 + 3(2sin(3\u03c0(-4(-5(-3x^2 + 3x + 5) + 4)^2 + 4(-5(-3x^2 + 3x + 5) + 4) - 4) - 3) - 3) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "178", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1e^(-2((-1(2|(-1|(1|x - 2| - 1) - 1| - 1) + 1| - 1) - 1)/(-2(2|(-1|(1|x - 2| - 1) - 1| - 1) + 1| - 1)))) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(2|(-3(3(-2x^2 - 4x + 2)) + 4) + 1| - 2) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2((3((-3(2|(-4x^2 + 5x + 2) + 3| - 2))/(-2(2|(-4x^2 + 5x + 2) + 3| - 2) + 1)))/(3((-3(2|(-4x^2 + 5x + 2) + 3| - 2))/(-2(2|(-4x^2 + 5x + 2) + 3| - 2) + 1)) - 2)) - 3)/(-1((3((-3(2|(-4x^2 + 5x + 2) + 3| - 2))/(-2(2|(-4x^2 + 5x + 2) + 3| - 2) + 1)))/(3((-3(2|(-4x^2 + 5x + 2) + 3| - 2))/(-2(2|(-4x^2 + 5x + 2) + 3| - 2) + 1)) - 2)) - 3) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(2\u03c0(-1(-5(1(1|x + 3| + 1)^2 + 3(1|x + 3| + 1))^2 + 1(1(1|x + 3| + 1)^2 + 3(1|x + 3| + 1)) - 2)^2 + 3)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "50", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(1\u03c0(1(1(-1(2|x - 1|) - 3) - 4) + 2) - 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "20", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1(-1(-1(2sin(2\u03c0(2|x - 1| + 3) - 2) + 1)^2 + 4(2sin(2\u03c0(2|x - 1| + 3) - 2) + 1) + 4)^2 - 5(-1(2sin(2\u03c0(2|x - 1| + 3) - 2) + 1)^2 + 4(2sin(2\u03c0(2|x - 1| + 3) - 2) + 1) + 4) + 3)^2 + 2(-1(-1(2sin(2\u03c0(2|x - 1| + 3) - 2) + 1)^2 + 4(2sin(2\u03c0(2|x - 1| + 3) - 2) + 1) + 4)^2 - 5(-1(2sin(2\u03c0(2|x - 1| + 3) - 2) + 1)^2 + 4(2sin(2\u03c0(2|x - 1| + 3) - 2) + 1) + 4) + 3) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "158", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(-2sin(2\u03c0(-2|(-3((1x + 2)/(1x)) + 2) + 3|) + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "99", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2((2(2cos(2\u03c0((-1(-5x^2 + 2x - 2) - 1)/(-2(-5x^2 + 2x - 2) - 3)) + 1)) - 1)/(-3(2cos(2\u03c0((-1(-5x^2 + 2x - 2) - 1)/(-2(-5x^2 + 2x - 2) - 3)) + 1)) + 2)) + 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (-1(-3(-2|(-3|((-1x + 3)/(-3x))|) + 2| + 1)^2 - 5(-2|(-3|((-1x + 3)/(-3x))|) + 2| + 1) + 2) - 3)/(-3(-3(-2|(-3|((-1x + 3)/(-3x))|) + 2| + 1)^2 - 5(-2|(-3|((-1x + 3)/(-3x))|) + 2| + 1) + 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2sin(1\u03c0(-2(-4(-2|((-2x + 1)/(-1x - 2))| + 1)^2 + 3(-2|((-2x + 1)/(-1x - 2))| + 1) - 3)^2 - 2(-4(-2|((-2x + 1)/(-1x - 2))| + 1)^2 + 3(-2|((-2x + 1)/(-1x - 2))| + 1) - 3) - 4)) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1075", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(1(-4(3(3x + 2)^2 + 5(3x + 2) - 1)^2 + 2(3(3x + 2)^2 + 5(3x + 2) - 1) + 3)^2 + 2(-4(3(3x + 2)^2 + 5(3x + 2) - 1)^2 + 2(3(3x + 2)^2 + 5(3x + 2) - 1) + 3) + 4) - 3| - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(3(-4(3((-2x - 1)/(-2x + 3))^2 + 4((-2x - 1)/(-2x + 3)) - 4)^2 - 1(3((-2x - 1)/(-2x + 3))^2 + 4((-2x - 1)/(-2x + 3)) - 4) + 5)^2 - 3(-4(3((-2x - 1)/(-2x + 3))^2 + 4((-2x - 1)/(-2x + 3)) - 4)^2 - 1(3((-2x - 1)/(-2x + 3))^2 + 4((-2x - 1)/(-2x + 3)) - 4) + 5) - 4)^2 + 4(3(-4(3((-2x - 1)/(-2x + 3))^2 + 4((-2x - 1)/(-2x + 3)) - 4)^2 - 1(3((-2x - 1)/(-2x + 3))^2 + 4((-2x - 1)/(-2x + 3)) - 4) + 5)^2 - 3(-4(3((-2x - 1)/(-2x + 3))^2 + 4((-2x - 1)/(-2x + 3)) - 4)^2 - 1(3((-2x - 1)/(-2x + 3))^2 + 4((-2x - 1)/(-2x + 3)) - 4) + 5) - 4) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 2(1|(1(1cos(2\u03c0(2|x + 1| + 3) - 3))^2 - 1(1cos(2\u03c0(2|x + 1| + 3) - 3)) - 1) + 3| - 1) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "80", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-3sin(2\u03c0(1|(-1|(5x^2 + 1x - 5) - 2|) + 1| + 1)) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1123", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1cos(1\u03c0(-4(-3(-2|((-1x - 2)/(-2x - 2)) + 2| + 2)^2 + 1(-2|((-1x - 2)/(-2x - 2)) + 2| + 2) - 5)^2 + 2(-3(-2|((-1x - 2)/(-2x - 2)) + 2| + 2)^2 + 1(-2|((-1x - 2)/(-2x - 2)) + 2| + 2) - 5))) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1064", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-3sin(3\u03c0(5(-2((-2x - 2)/(-1x + 2))^2 + 5((-2x - 2)/(-1x + 2)) + 4)^2 - 5(-2((-2x - 2)/(-1x + 2))^2 + 5((-2x - 2)/(-1x + 2)) + 4) + 1) + 1) - 1) + 1| equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "91", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1|(2(-1|(2cos(3\u03c0(-5x^2 - 3x - 2) + 1) + 3) - 1| - 1)^2 + 2(-1|(2cos(3\u03c0(-5x^2 - 3x - 2) + 1) + 3) - 1| - 1) - 4)| where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(-1e^(-2(-2(-3|((-3x - 2)/(2x)) + 3| + 1)^2 - 3(-3|((-3x - 2)/(2x)) + 3| + 1) + 2)) + 3) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2cos(3\u03c0(-3(3|(2|(-4x - 4) + 2| + 2) + 3| - 2) - 3) - 2) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1925", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(-5((2(-2(2|x + 1| - 1) + 1) + 3)/(-1(-2(2|x + 1| - 1) + 1))) - 3) - 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(2(-3|(4((2x - 3)/(2x + 2)) + 2) + 2|) + 2) - 1| - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(4(-1(3(-2x + 5))^2 - 3(3(-2x + 5)) + 4) + 3) - 2| - 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1|((-2(-4(1|x - 2| - 1) - 3) + 2)/(-3(-4(1|x - 2| - 1) - 3) - 3)) - 2| - 2) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-1(-3(2(1cos(2\u03c0((2x + 2)/(3x - 1)) - 1) + 1) - 3) - 5) - 3)/(-3(-3(2(1cos(2\u03c0((2x + 2)/(3x - 1)) - 1) + 1) - 3) - 5) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "42", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2sin(2\u03c0(4(-5(3((1x - 1)/(1x + 3))^2 - 2((1x - 1)/(1x + 3)) - 1) - 2) - 5) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "776", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3|(-2(1(3e^(2(-4x^2 + 2x + 1)) + 3) - 5) + 3) + 2| - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3((-2(-1|(-1(-2|x + 2| + 2)^2 + 5(-2|x + 2| + 2) + 2)|) - 3)/(1(-1|(-1(-2|x + 2| + 2)^2 + 5(-2|x + 2| + 2) + 2)|) + 1)) + 1)/(2((-2(-1|(-1(-2|x + 2| + 2)^2 + 5(-2|x + 2| + 2) + 2)|) - 3)/(1(-1|(-1(-2|x + 2| + 2)^2 + 5(-2|x + 2| + 2) + 2)|) + 1)) - 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1|(3cos(1\u03c0(1(4((-2x - 1)/(-1x - 3))^2 + 3((-2x - 1)/(-1x - 3)) + 5) + 4) - 3) - 2) + 2| - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "323", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((-1((-2(1|(2x^2 + 5x - 3)| - 3) - 3)/(-3(1|(2x^2 + 5x - 3)| - 3) + 2)) + 2)/(1((-2(1|(2x^2 + 5x - 3)| - 3) - 3)/(-3(1|(2x^2 + 5x - 3)| - 3) + 2)) + 3)) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2|(1|(1|(-5((-2x + 3)/(-3x - 1))^2 + 3((-2x + 3)/(-3x - 1)) + 4) - 2| + 2) - 2| - 1) - 2| - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3sin(2\u03c0(3|(-1(-1((3x - 1)/(1x - 2))^2 - 4((3x - 1)/(1x - 2)) + 5)^2 - 3(-1((3x - 1)/(1x - 2))^2 - 4((3x - 1)/(1x - 2)) + 5) - 4) + 2| + 3) - 3) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "888", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2|((-3(-3((-3((-1x + 2)/(1x)) + 2)/(-3((-1x + 2)/(1x)) - 1))^2 + 4((-3((-1x + 2)/(1x)) + 2)/(-3((-1x + 2)/(1x)) - 1))) + 3)/(3(-3((-3((-1x + 2)/(1x)) + 2)/(-3((-1x + 2)/(1x)) - 1))^2 + 4((-3((-1x + 2)/(1x)) + 2)/(-3((-1x + 2)/(1x)) - 1))))) - 3| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -5(3sin(2\u03c0(4((1(5x^2 - 5x + 3) - 3)/(-2(5x^2 - 5x + 3) + 1))^2 + 4((1(5x^2 - 5x + 3) - 3)/(-2(5x^2 - 5x + 3) + 1)) - 2) - 1) + 2)^2 - 5(3sin(2\u03c0(4((1(5x^2 - 5x + 3) - 3)/(-2(5x^2 - 5x + 3) + 1))^2 + 4((1(5x^2 - 5x + 3) - 3)/(-2(5x^2 - 5x + 3) + 1)) - 2) - 1) + 2) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -2(-3((-3(2cos(3\u03c0(-3|x - 3| + 2)) + 1) + 2)/(1(2cos(3\u03c0(-3|x - 3| + 2)) + 1))) + 2)^2 - 3(-3((-3(2cos(3\u03c0(-3|x - 3| + 2)) + 1) + 2)/(1(2cos(3\u03c0(-3|x - 3| + 2)) + 1))) + 2) + 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "170", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3cos(2\u03c0(-3(3|(-3(1x + 3)^2 + 4(1x + 3) + 4)|)^2 + 3(3|(-3(1x + 3)^2 + 4(1x + 3) + 4)|) - 3) - 3) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "591", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1((1(3sin(1\u03c0(1((2x + 1)/(2x))^2 + 3((2x + 1)/(2x)) - 2) + 2) + 1) - 3)/(2(3sin(1\u03c0(1((2x + 1)/(2x))^2 + 3((2x + 1)/(2x)) - 2) + 2) + 1) - 3)) - 3)/(1((1(3sin(1\u03c0(1((2x + 1)/(2x))^2 + 3((2x + 1)/(2x)) - 2) + 2) + 1) - 3)/(2(3sin(1\u03c0(1((2x + 1)/(2x))^2 + 3((2x + 1)/(2x)) - 2) + 2) + 1) - 3)) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "16", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5(-1(2((2(2e^(1x)))/(-3(2e^(1x)) + 4)) + 5)^2 - 1(2((2(2e^(1x)))/(-3(2e^(1x)) + 4)) + 5) + 5)^2 + 4(-1(2((2(2e^(1x)))/(-3(2e^(1x)) + 4)) + 5)^2 - 1(2((2(2e^(1x)))/(-3(2e^(1x)) + 4)) + 5) + 5) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-3sin(2\u03c0(3(-1|(1|x + 2| + 3) - 3| - 1) + 1) + 2))^2 + 4(-3sin(2\u03c0(3(-1|(1|x + 2| + 3) - 3| - 1) + 1) + 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (-3(-1|((1(1(-1|x + 3| - 1)^2 + 5(-1|x + 3| - 1) + 5) + 3)/(2(1(-1|x + 3| - 1)^2 + 5(-1|x + 3| - 1) + 5) + 2))| + 2))/(2(-1|((1(1(-1|x + 3| - 1)^2 + 5(-1|x + 3| - 1) + 5) + 3)/(2(1(-1|x + 3| - 1)^2 + 5(-1|x + 3| - 1) + 5) + 2))| + 2) + 3) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2|((2(-2|(5(1x^2 + 3x - 3) + 5) - 3| - 1) - 3)/(-1(-2|(5(1x^2 + 3x - 3) + 5) - 3| - 1) - 1)) + 3| - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(1(-2(-1sin(1\u03c0(-1|x + 1| + 1)) + 3) + 5)^2 - 3(-2(-1sin(1\u03c0(-1|x + 1| + 1)) + 3) + 5) + 3) - 2| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "22", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(5((3((1((3x - 2)/(-1x - 3)) - 2)/(2((3x - 2)/(-1x - 3)))) + 1)/(-2((1((3x - 2)/(-1x - 3)) - 2)/(2((3x - 2)/(-1x - 3)))) - 1))^2 + 5((3((1((3x - 2)/(-1x - 3)) - 2)/(2((3x - 2)/(-1x - 3)))) + 1)/(-2((1((3x - 2)/(-1x - 3)) - 2)/(2((3x - 2)/(-1x - 3)))) - 1)) - 3)^2 - 4(5((3((1((3x - 2)/(-1x - 3)) - 2)/(2((3x - 2)/(-1x - 3)))) + 1)/(-2((1((3x - 2)/(-1x - 3)) - 2)/(2((3x - 2)/(-1x - 3)))) - 1))^2 + 5((3((1((3x - 2)/(-1x - 3)) - 2)/(2((3x - 2)/(-1x - 3)))) + 1)/(-2((1((3x - 2)/(-1x - 3)) - 2)/(2((3x - 2)/(-1x - 3)))) - 1)) - 3) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(-3cos(1\u03c0(-5(2(-3x^2 + 5x + 3) - 5) - 3)) + 3)^2 - 4(-3cos(1\u03c0(-5(2(-3x^2 + 5x + 3) - 5) - 3)) + 3) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1199", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (2(-1(1((2(2cos(1\u03c0x + 1) - 1) + 3)/(-3(2cos(1\u03c0x + 1) - 1) - 3)) + 4) + 2) + 3)/(3(-1(1((2(2cos(1\u03c0x + 1) - 1) + 3)/(-3(2cos(1\u03c0x + 1) - 1) - 3)) + 4) + 2) - 1) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1cos(2\u03c0(-3|(3|(-1|((2x + 1)/(1x + 1))| - 3) + 1| + 1) + 3| - 3) - 2) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "87", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(-3cos(3\u03c0((-1((-2((2x - 3)/(3x - 2)) + 1)/(3((2x - 3)/(3x - 2)))) - 3)/(1((-2((2x - 3)/(3x - 2)) + 1)/(3((2x - 3)/(3x - 2)))) - 2)) - 3) + 2) - 4 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "35", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((-2(3cos(1\u03c0(2|((2x - 2)/(3x - 2)) + 1| - 3) + 3)) - 1)/(1(3cos(1\u03c0(2|((2x - 2)/(3x - 2)) + 1| - 3) + 3)))) - 1)/(-1((-2(3cos(1\u03c0(2|((2x - 2)/(3x - 2)) + 1| - 3) + 3)) - 1)/(1(3cos(1\u03c0(2|((2x - 2)/(3x - 2)) + 1| - 3) + 3)))) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "10", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3((2(-1cos(2\u03c0(-1((2x)/(3x - 1))^2 - 2((2x)/(3x - 1)))) + 1) - 3)/(-3(-1cos(2\u03c0(-1((2x)/(3x - 1))^2 - 2((2x)/(3x - 1)))) + 1) - 1))^2 + 1((2(-1cos(2\u03c0(-1((2x)/(3x - 1))^2 - 2((2x)/(3x - 1)))) + 1) - 3)/(-3(-1cos(2\u03c0(-1((2x)/(3x - 1))^2 - 2((2x)/(3x - 1)))) + 1) - 1)) + 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 4(1(-4(1|(-1x + 4)| + 1) + 5)^2 + 1(-4(1|(-1x + 4)| + 1) + 5))^2 + 5(1(-4(1|(-1x + 4)| + 1) + 5)^2 + 1(-4(1|(-1x + 4)| + 1) + 5)) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5((3(-1(3|((-2x - 1)/(-3x + 1)) + 1| - 3)^2 + 3(3|((-2x - 1)/(-3x + 1)) + 1| - 3) + 4) - 3)/(-3(-1(3|((-2x - 1)/(-3x + 1)) + 1| - 3)^2 + 3(3|((-2x - 1)/(-3x + 1)) + 1| - 3) + 4)))^2 + 1((3(-1(3|((-2x - 1)/(-3x + 1)) + 1| - 3)^2 + 3(3|((-2x - 1)/(-3x + 1)) + 1| - 3) + 4) - 3)/(-3(-1(3|((-2x - 1)/(-3x + 1)) + 1| - 3)^2 + 3(3|((-2x - 1)/(-3x + 1)) + 1| - 3) + 4))) + 2 have 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 number of x-intercepts of the function f(x) = 2(3cos(1\u03c0(-2|(-4(5x^2 + 2x - 3) + 3) + 1|) + 3) - 1) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1595", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 3(-1cos(2\u03c0((1(-4(4x + 5) + 5) + 2)/(3(-4(4x + 5) + 5))) - 3) + 2) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "5", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(5(5(-2|((-2x - 3)/(-2x + 1)) - 3|) + 2) - 5) - 1| + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 3(-5((-3(-2|(1|x - 1| + 1) - 3|))/(-1(-2|(1|x - 1| + 1) - 3|) + 2)) + 3)^2 + 5(-5((-3(-2|(1|x - 1| + 1) - 3|))/(-1(-2|(1|x - 1| + 1) - 3|) + 2)) + 3) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(-2sin(1\u03c0(-3(1(3x - 4) - 5)) - 1) - 1) - 4 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(3\u03c0((1(-3(-3|(-4x + 1) - 2| + 1) - 3) + 3)/(1(-3(-3|(-4x + 1) - 2| + 1) - 3) - 2)) + 1) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "27", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5((-2(-2cos(3\u03c0((-3((-2x + 2)/(-3x + 4)) - 2)/(3((-2x + 2)/(-3x + 4)) - 2)) + 2) - 1) - 3)/(-2(-2cos(3\u03c0((-3((-2x + 2)/(-3x + 4)) - 2)/(3((-2x + 2)/(-3x + 4)) - 2)) + 2) - 1) - 1)) - 5 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "360", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3sin(3\u03c0(-4(-3((1(-4x^2 - 4x - 5) - 3)/(-3(-4x^2 - 4x - 5) + 1))^2 + 3((1(-4x^2 - 4x - 5) - 3)/(-3(-4x^2 - 4x - 5) + 1)) - 3)^2 - 5(-3((1(-4x^2 - 4x - 5) - 3)/(-3(-4x^2 - 4x - 5) + 1))^2 + 3((1(-4x^2 - 4x - 5) - 3)/(-3(-4x^2 - 4x - 5) + 1)) - 3) - 2) + 3) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "234", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2cos(2\u03c0(-4(-1(1(3x^2 + 4x - 3)) - 5)^2 + 1(-1(1(3x^2 + 4x - 3)) - 5) - 3) + 3) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1083", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(1e^(-1(-1(-2|(-2|x + 1| + 2) + 3| - 2) - 4)) - 1) + 3 have 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 number of x-intercepts of the function f(x) = -3|(1|((3((2(1x^2 + 3x - 1) + 3)/(-3(1x^2 + 3x - 1) + 1)) - 3)/(-1((2(1x^2 + 3x - 1) + 3)/(-3(1x^2 + 3x - 1) + 1)) + 2)) + 2|) - 3| + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(1(-3(-1((3x + 2)/(-2x - 3))^2 + 2)^2 + 1(-1((3x + 2)/(-2x - 3))^2 + 2) + 5) - 3)^2 + 1(1(-3(-1((3x + 2)/(-2x - 3))^2 + 2)^2 + 1(-1((3x + 2)/(-2x - 3))^2 + 2) + 5) - 3) - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1(1(3e^(-1((3(-3|x - 3| + 2) + 3)/(1(-3|x - 3| + 2) - 3))) - 3)^2 + 5(3e^(-1((3(-3|x - 3| + 2) + 3)/(1(-3|x - 3| + 2) - 3))) - 3) - 4)^2 + 2(1(3e^(-1((3(-3|x - 3| + 2) + 3)/(1(-3|x - 3| + 2) - 3))) - 3)^2 + 5(3e^(-1((3(-3|x - 3| + 2) + 3)/(1(-3|x - 3| + 2) - 3))) - 3) - 4) - 4 have 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 number of x-intercepts of the function f(x) = 3(4((2((-2(-3sin(3\u03c0x - 2) - 1))/(2(-3sin(3\u03c0x - 2) - 1) + 1)) + 3)/(1((-2(-3sin(3\u03c0x - 2) - 1))/(2(-3sin(3\u03c0x - 2) - 1) + 1))))^2 - 4((2((-2(-3sin(3\u03c0x - 2) - 1))/(2(-3sin(3\u03c0x - 2) - 1) + 1)) + 3)/(1((-2(-3sin(3\u03c0x - 2) - 1))/(2(-3sin(3\u03c0x - 2) - 1) + 1)))) - 1) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (-3(4(-1(-2|((-1x - 3)/(2x + 3)) - 1| - 1)^2 - 4(-2|((-1x - 3)/(2x + 3)) - 1| - 1) - 1)^2 - 4(-1(-2|((-1x - 3)/(2x + 3)) - 1| - 1)^2 - 4(-2|((-1x - 3)/(2x + 3)) - 1| - 1) - 1) + 1) + 2)/(2(4(-1(-2|((-1x - 3)/(2x + 3)) - 1| - 1)^2 - 4(-2|((-1x - 3)/(2x + 3)) - 1| - 1) - 1)^2 - 4(-1(-2|((-1x - 3)/(2x + 3)) - 1| - 1)^2 - 4(-2|((-1x - 3)/(2x + 3)) - 1| - 1) - 1) + 1) - 3) have 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 number of x-intercepts of the function f(x) = 3|(3cos(2\u03c0(4(1|(-3x^2 + 1x + 4) + 1| - 3) - 5) - 2) + 1) + 1| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "577", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 2((3(2|(-2cos(2\u03c0(-3x^2 + 4x + 1) + 3) + 1) - 3| - 1))/(2(2|(-2cos(2\u03c0(-3x^2 + 4x + 1) + 3) + 1) - 3| - 1) - 3))^2 + 5((3(2|(-2cos(2\u03c0(-3x^2 + 4x + 1) + 3) + 1) - 3| - 1))/(2(2|(-2cos(2\u03c0(-3x^2 + 4x + 1) + 3) + 1) - 3| - 1) - 3)) - 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "735", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3cos(1\u03c0(1(-4(-5((-1x + 3)/(1x))^2 + 2((-1x + 3)/(1x)) + 5)^2 + 2(-5((-1x + 3)/(1x))^2 + 2((-1x + 3)/(1x)) + 5) + 2))) + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "781", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (2(-2|(-5(4((-1x + 3)/(2x + 2)) - 5)^2 - 4(4((-1x + 3)/(2x + 2)) - 5) + 5) - 1| + 3) + 1)/(-1(-2|(-5(4((-1x + 3)/(2x + 2)) - 5)^2 - 4(4((-1x + 3)/(2x + 2)) - 5) + 5) - 1| + 3) + 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-1(5(3(1x^2 + 4x - 1)^2 - 4(1x^2 + 4x - 1) - 2) - 2)^2 + 4(5(3(1x^2 + 4x - 1)^2 - 4(1x^2 + 4x - 1) - 2) - 2) + 5) - 2| + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "12", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (1(-3sin(1\u03c0((-3(-1|((-1x - 2)/(3x + 1)) + 2| + 3))/(-1(-1|((-1x - 2)/(3x + 1)) + 2| + 3) + 2)) - 1) - 1))/(-2(-3sin(1\u03c0((-3(-1|((-1x - 2)/(3x + 1)) + 2| + 3))/(-1(-1|((-1x - 2)/(3x + 1)) + 2| + 3) + 2)) - 1) - 1) - 3) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "72", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1cos(3\u03c0((3(1(-3(-4x - 3)^2 - 4(-4x - 3) - 3) + 2) - 2)/(-2(1(-3(-4x - 3)^2 - 4(-4x - 3) - 3) + 2) + 1)) + 3) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "6", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 1cos(2\u03c0(-4(2|(2|((3x - 1)/(2x)) - 2|) - 2| + 3) - 1) - 2) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "82", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-3(-1(5(-2|x - 1| + 2) - 2)^2 + 1(5(-2|x - 1| + 2) - 2) + 1) + 4) + 1| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -4(3(-3(2|(2|x + 3|)| - 3)) + 4)^2 - 3(3(-3(2|(2|x + 3|)| - 3)) + 4) + 2 have 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 number of x-intercepts of the function f(x) = (-3(-3|(3|(1(-4x - 4)^2 - 4(-4x - 4) - 5)| - 1) + 1| + 2) - 2)/(1(-3|(3|(1(-4x - 4)^2 - 4(-4x - 4) - 5)| - 1) + 1| + 2) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2((2((-2((-1(1cos(3\u03c0x - 2) + 3) + 2)/(1(1cos(3\u03c0x - 2) + 3) + 1)) - 1)/(-2((-1(1cos(3\u03c0x - 2) + 3) + 2)/(1(1cos(3\u03c0x - 2) + 3) + 1)) - 3)) - 1)/(1((-2((-1(1cos(3\u03c0x - 2) + 3) + 2)/(1(1cos(3\u03c0x - 2) + 3) + 1)) - 1)/(-2((-1(1cos(3\u03c0x - 2) + 3) + 2)/(1(1cos(3\u03c0x - 2) + 3) + 1)) - 3)) + 1)) - 1)/(-2((2((-2((-1(1cos(3\u03c0x - 2) + 3) + 2)/(1(1cos(3\u03c0x - 2) + 3) + 1)) - 1)/(-2((-1(1cos(3\u03c0x - 2) + 3) + 2)/(1(1cos(3\u03c0x - 2) + 3) + 1)) - 3)) - 1)/(1((-2((-1(1cos(3\u03c0x - 2) + 3) + 2)/(1(1cos(3\u03c0x - 2) + 3) + 1)) - 1)/(-2((-1(1cos(3\u03c0x - 2) + 3) + 2)/(1(1cos(3\u03c0x - 2) + 3) + 1)) - 3)) + 1))) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "60", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2cos(3\u03c0(3|((-1(1((-3x + 2)/(1x))^2 + 4((-3x + 2)/(1x)) - 4) + 1)/(-1(1((-3x + 2)/(1x))^2 + 4((-3x + 2)/(1x)) - 4))) + 3| - 2) + 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "29", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -1|(-5(-4(2|(-3sin(3\u03c0x)) + 3| - 3)^2 - 3(2|(-3sin(3\u03c0x)) + 3| - 3) + 3) + 3) - 3| + 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "95", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = 4(-3|((-2(2e^(1(2|x| - 3)) - 1) - 2)/(1(2e^(1(2|x| - 3)) - 1) - 3)) - 1| + 1)^2 - 5 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (-2(5(-1|(-1|(-4x^2 + 5x + 1) + 3| + 3) + 1|) + 2) + 2)/(-2(5(-1|(-1|(-4x^2 + 5x + 1) + 3| + 3) + 1|) + 2)) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 3|(5(2(-1(-1x^2 + 3x - 1) - 2)^2 + 1(-1(-1x^2 + 3x - 1) - 2) - 3) + 3) + 2| - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -2cos(3\u03c0(-3|((1((-1((-1x + 1)/(-1x - 3)) + 1)/(1((-1x + 1)/(-1x - 3)))) - 3)/(-1((-1((-1x + 1)/(-1x - 3)) + 1)/(1((-1x + 1)/(-1x - 3)))) + 2)) + 2| - 2) + 1) - 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "104", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3(-1cos(3\u03c0(1|(-1(-3x + 5) + 4) + 2| + 2) + 1) - 1)^2 - 5(-1cos(3\u03c0(1|(-1(-3x + 5) + 4) + 2| + 2) + 1) - 1) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "362", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -3(-3cos(2\u03c0(-2|(1(-5x + 2) + 3) - 2| + 3) - 1) + 3) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "400", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 1(-1|(1(-2cos(3\u03c0(-3|x| + 2) - 1) + 1)^2 - 3(-2cos(3\u03c0(-3|x| + 2) - 1) + 1) + 2) + 2| + 2)^2 + 3(-1|(1(-2cos(3\u03c0(-3|x| + 2) - 1) + 1)^2 - 3(-2cos(3\u03c0(-3|x| + 2) - 1) + 1) + 2) + 2| + 2) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "180", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (3(1(3|(2|(-3|x + 3| + 1) + 1| + 1) + 1| - 2) - 5) - 3)/(2(1(3|(2|(-3|x + 3| + 1) + 1| + 1) + 1| - 2) - 5) + 2) where -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 number of x-intercepts of the function f(x) = 2(-1sin(3\u03c0(-5(4(4x - 2)^2 - 5(4x - 2) - 2) + 1) - 3))^2 + 5(-1sin(3\u03c0(-5(4(4x - 2)^2 - 5(4x - 2) - 2) + 1) - 3)) - 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "882", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 2(-1cos(3\u03c0(5(4(4x^2 + 1x + 5))) + 2) - 3)^2 + 3(-1cos(3\u03c0(5(4(4x^2 + 1x + 5))) + 2) - 3) - 5 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1379", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -5((1(3(-3|((3x - 2)/(-2x + 1)) + 3| + 2)^2 + 4(-3|((3x - 2)/(-2x + 1)) + 3| + 2) - 4) + 2)/(1(3(-3|((3x - 2)/(-2x + 1)) + 3| + 2)^2 + 4(-3|((3x - 2)/(-2x + 1)) + 3| + 2) - 4)))^2 + 3((1(3(-3|((3x - 2)/(-2x + 1)) + 3| + 2)^2 + 4(-3|((3x - 2)/(-2x + 1)) + 3| + 2) - 4) + 2)/(1(3(-3|((3x - 2)/(-2x + 1)) + 3| + 2)^2 + 4(-3|((3x - 2)/(-2x + 1)) + 3| + 2) - 4))) + 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "7", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(-3sin(2\u03c0((-3((2(-4x - 1) - 1)/(-2(-4x - 1) - 3)) - 1)/(3((2(-4x - 1) - 1)/(-2(-4x - 1) - 3)))) - 1)) - 3)/(3(-3sin(2\u03c0((-3((2(-4x - 1) - 1)/(-2(-4x - 1) - 3)) - 1)/(3((2(-4x - 1) - 1)/(-2(-4x - 1) - 3)))) - 1)) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "9", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 1(-1|((-1(5(3sin(1\u03c0x - 3) - 2) + 2) - 3)/(2(5(3sin(1\u03c0x - 3) - 2) + 2) + 2)) + 3| + 2)^2 - 4(-1|((-1(5(3sin(1\u03c0x - 3) - 2) + 2) - 3)/(2(5(3sin(1\u03c0x - 3) - 2) + 2) + 2)) + 3| + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "40", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|(-5(2|((1((-3x)/(3x + 2)) + 3)/(-1((-3x)/(3x + 2)) + 2)) - 3| - 2)^2 + 2(2|((1((-3x)/(3x + 2)) + 3)/(-1((-3x)/(3x + 2)) + 2)) - 3| - 2)) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|(-2(1(2(2|x - 1| - 2) - 3) + 2) - 1)| - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (1((2(1|(2e^(-1(-3x^2 - 4x - 2)) + 2)| + 1) - 2)/(-2(1|(2e^(-1(-3x^2 - 4x - 2)) + 2)| + 1) - 1)) + 1)/(2((2(1|(2e^(-1(-3x^2 - 4x - 2)) + 2)| + 1) - 2)/(-2(1|(2e^(-1(-3x^2 - 4x - 2)) + 2)| + 1) - 1)) + 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "17", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = (3(-3|((-1((2(1x^2 + 5x - 5) + 1)/(-2(1x^2 + 5x - 5) + 3)))/(-1((2(1x^2 + 5x - 5) + 1)/(-2(1x^2 + 5x - 5) + 3)) + 2))| + 1) + 2)/(3(-3|((-1((2(1x^2 + 5x - 5) + 1)/(-2(1x^2 + 5x - 5) + 3)))/(-1((2(1x^2 + 5x - 5) + 1)/(-2(1x^2 + 5x - 5) + 3)) + 2))| + 1) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2(1(2|(3(1x^2 - 3x - 1)^2 + 4(1x^2 - 3x - 1)) + 1| - 1) - 1)^2 + 4(1(2|(3(1x^2 - 3x - 1)^2 + 4(1x^2 - 3x - 1)) + 1| - 1) - 1) + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1(1cos(3\u03c0(-5(4((-2x + 1)/(-2x - 2))^2 + 4((-2x + 1)/(-2x - 2)) + 2) - 1) - 2) - 1)^2 - 2(1cos(3\u03c0(-5(4((-2x + 1)/(-2x - 2))^2 + 4((-2x + 1)/(-2x - 2)) + 2) - 1) - 2) - 1) - 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "479", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(-1((3(1(1cos(3\u03c0x - 2) + 3) - 2) - 1)/(2(1(1cos(3\u03c0x - 2) + 3) - 2) + 1))^2 + 5((3(1(1cos(3\u03c0x - 2) + 3) - 2) - 1)/(2(1(1cos(3\u03c0x - 2) + 3) - 2) + 1)))^2 - 5(-1((3(1(1cos(3\u03c0x - 2) + 3) - 2) - 1)/(2(1(1cos(3\u03c0x - 2) + 3) - 2) + 1))^2 + 5((3(1(1cos(3\u03c0x - 2) + 3) - 2) - 1)/(2(1(1cos(3\u03c0x - 2) + 3) - 2) + 1))) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "120", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4((-2((2(3cos(2\u03c0((3x)/(-1x - 1)) - 1) + 2) - 2)/(-2(3cos(2\u03c0((3x)/(-1x - 1)) - 1) + 2) - 2)) + 3)/(-2((2(3cos(2\u03c0((3x)/(-1x - 1)) - 1) + 2) - 2)/(-2(3cos(2\u03c0((3x)/(-1x - 1)) - 1) + 2) - 2)))) - 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "63", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2|((-3(2(2(1x^2 + 4x) - 5)^2 - 4(2(1x^2 + 4x) - 5) - 2) + 2)/(1(2(2(1x^2 + 4x) - 5)^2 - 4(2(1x^2 + 4x) - 5) - 2) - 3)) - 2| + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(1|(2(-3|(4x - 1) - 1| + 2) - 1) + 1| - 3) - 1) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-4((-2(3(-2x^2 + 4x + 3) - 1))/(-1(3(-2x^2 + 4x + 3) - 1) - 3))^2 + 3((-2(3(-2x^2 + 4x + 3) - 1))/(-1(3(-2x^2 + 4x + 3) - 1) - 3)) - 2)^2 + 5(-4((-2(3(-2x^2 + 4x + 3) - 1))/(-1(3(-2x^2 + 4x + 3) - 1) - 3))^2 + 3((-2(3(-2x^2 + 4x + 3) - 1))/(-1(3(-2x^2 + 4x + 3) - 1) - 3)) - 2) - 4 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation 5(-2sin(1\u03c0(2|(4(-1|x + 3|) + 3) - 3| - 2) + 3) - 1) - 1 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "160", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = (1(-3(-2(-5(2x^2 + 2x - 2)^2 + 4(2x^2 + 2x - 2) + 3)^2 + 4(-5(2x^2 + 2x - 2)^2 + 4(2x^2 + 2x - 2) + 3) - 3) - 3) - 2)/(-3(-3(-2(-5(2x^2 + 2x - 2)^2 + 4(2x^2 + 2x - 2) + 3)^2 + 4(-5(2x^2 + 2x - 2)^2 + 4(2x^2 + 2x - 2) + 3) - 3) - 3) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -2sin(1\u03c0(-2(-2|(4((-1x + 1)/(2x)) - 1) + 2| + 2)^2 - 1(-2|(4((-1x + 1)/(2x)) - 1) + 2| + 2) - 4) - 1) - 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "115", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3(4(3(-3sin(2\u03c0(2x^2 - 5x - 3) + 3) + 1)^2 + 2(-3sin(2\u03c0(2x^2 - 5x - 3) + 3) + 1) - 5) - 4) + 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1196", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(1sin(1\u03c0(2|((2(-4x + 1) - 1)/(-1(-4x + 1) + 2)) - 3| + 1) - 1) + 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation -3e^(1(3|((-2((-1(1x^2 + 5x - 1) + 1)/(-2(1x^2 + 5x - 1) + 3)) - 2)/(3((-1(1x^2 + 5x - 1) + 1)/(-2(1x^2 + 5x - 1) + 3)) + 1)) + 2| - 2)) + 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 3(1|(-3(2e^(2((2x - 1)/(1x - 2))) - 2) - 1)| - 2)^2 - 3(1|(-3(2e^(2((2x - 1)/(1x - 2))) - 2) - 1)| - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "4", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5(1|(-2(1(2x)^2 - 4(2x) - 2) - 5) + 3| - 1)^2 - 4(1|(-2(1(2x)^2 - 4(2x) - 2) - 5) + 3| - 1) - 4 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "8", "dataset": "MATH"}
{"messages": [{"content": "How many solutions does the equation (2(3sin(3\u03c0(1|(-3((-1x - 2)/(-3x))^2 - 4((-1x - 2)/(-3x)) + 4) - 1| + 1) - 2) - 2) + 3)/(-1(3sin(3\u03c0(1|(-3((-1x - 2)/(-3x))^2 - 4((-1x - 2)/(-3x)) + 4) - 1| + 1) - 2) - 2) - 2) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "56", "dataset": "MATH"}
{"messages": [{"content": "How many zeros does the function f(x) = -5(-3sin(2\u03c0(-2|(2(-1x + 1)^2 + 5(-1x + 1) - 5) + 2| + 2) + 3) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1296", "dataset": "MATH"}
{"messages": [{"content": "Find the number of x-intercepts of the function f(x) = (2(2|(3cos(1\u03c0((-1((-1x - 2)/(1x)) - 2)/(-2((-1x - 2)/(1x)) - 3)) + 1) + 1)| - 1) - 1)/(-2(2|(3cos(1\u03c0((-1((-1x - 2)/(1x)) - 2)/(-2((-1x - 2)/(1x)) - 3)) + 1) + 1)| - 1) - 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "54", "dataset": "MATH"}