| {"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -2sin(1\u03c0(-5(-1(2|x + 1| - 3) - 1)^2 + 1(-1(2|x + 1| - 3) - 1) + 4) + 3) 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": "Determine the number of values x in [-10, 10] where f(x) = (-2(1|(-3x^2 + 4x + 1) - 2| - 1) - 2)/(-3(1|(-3x^2 + 4x + 1) - 2| - 1) - 2) equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -5(-2cos(3\u03c0(2(-1|x - 1| + 2) + 1) - 3))^2 - 4(-2cos(3\u03c0(2(-1|x - 1| + 2) + 1) - 3)) + 3 equals zero.\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) = -2(-2(3|x - 2| - 1)^2 + 3(3|x - 2| - 1) + 5) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = -3(2e^(2(2|x| - 1)) - 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many solutions does the equation 3cos(3\u03c0((2(-1|(-5x - 2) - 2| + 1) + 1)/(1(-1|(-5x - 2) - 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": "110", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3sin(3\u03c0(5(-2|(-3((-1x - 1)/(-3x - 2))^2 + 4((-1x - 1)/(-3x - 2)) - 4) - 1| + 3) - 3)) - 1 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "83", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(2\u03c0(-2((3(1|x + 1| - 1))/(-2(1|x + 1| - 1) + 3)) - 2) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "201", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = -3|(2cos(1\u03c0(1x - 1) - 3) + 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": "Find the number of x-intercepts of the function f(x) = -2(1(-1|x - 1| - 2) + 2)^2 - 4(1(-1|x - 1| - 2) + 2) + 1 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 2|((1(-5(3cos(3\u03c0x))^2 + 3))/(3(-5(3cos(3\u03c0x))^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": "92", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = (-1(-1(2sin(1\u03c0x - 1) - 3) + 2) + 3)/(-1(-1(2sin(1\u03c0x - 1) - 3) + 2) + 2) 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": "Find the number of x-intercepts of the function f(x) = -4(-3cos(1\u03c0(-3|(4x^2 - 3x) - 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": "1583", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -4(3sin(3\u03c0(4((3(-1|x + 2| + 2) - 3)/(-1(-1|x + 2| + 2) - 3))^2 + 5((3(-1|x + 2| + 2) - 3)/(-1(-1|x + 2| + 2) - 3)) - 2) + 2) + 2) + 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "1038", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -1e^(2((2(-3|(-5x^2 - 2x + 2) - 2| + 2) - 1)/(-3(-3|(-5x^2 - 2x + 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": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = -2sin(1\u03c0(1(-2x - 5)^2 - 1(-2x - 5) - 1)) + 1 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "833", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -1|(2(-5((-3x + 1)/(3x)) + 5)^2 - 2(-5((-3x + 1)/(3x)) + 5) - 3) + 1| + 3 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = 1sin(1\u03c0(-3|(5x - 4)| + 1) - 1) - 1 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 solutions does the equation 4(2|((1(-1x^2 - 5x))/(-3(-1x^2 - 5x) + 2)) - 3| - 1) = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = (-2(-5(5x^2 + 3x - 2) + 2) + 2)/(-1(-5(5x^2 + 3x - 2) + 2) + 2) have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = -1|(-2(1cos(3\u03c0((1x - 1)/(-2x - 1))) + 1)^2 - 4(1cos(3\u03c0((1x - 1)/(-2x - 1))) + 1) + 3) - 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(2\u03c0((2(-1(1|x| + 2)^2 + 3(1|x| + 2)) + 1)/(2(-1(1|x| + 2)^2 + 3(1|x| + 2)) + 3)) + 3) - 3) + 5 where -10 \u2264 x \u2264 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(-2sin(3\u03c0(-4x - 4) + 3) + 1)^2 - 3(-2sin(3\u03c0(-4x - 4) + 3) + 1) - 3 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "480", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the number of x-intercepts of the function f(x) = -3cos(1\u03c0(2|(2((2x + 1)/(-1x + 2))^2 + 1((2x + 1)/(-1x + 2)) - 4) + 2| - 1) - 1) - 2 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "272", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = 2(5(3cos(2\u03c0x + 1) + 1) - 5)^2 - 2(5(3cos(2\u03c0x + 1) + 1) - 5) - 1 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) = 3cos(1\u03c0(-1(-1|(-1x - 2) + 2| + 1)^2 - 2(-1|(-1x - 2) + 2| + 1) + 5)) + 2 equals zero.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "136", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = -3|(2(1cos(2\u03c0(-1x - 2) + 3) + 2)^2 - 5(1cos(2\u03c0(-1x - 2) + 3) + 2) - 4) + 2| + 3 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 -1(-3cos(2\u03c0((2x + 3)/(2x + 1)) - 2))^2 + 4(-3cos(2\u03c0((2x + 3)/(2x + 1)) - 2)) - 2 = 0 have in the range [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "45", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 5((1(5x^2 - 4x) - 1)/(3(5x^2 - 4x) - 2)) + 5 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "Find the number of x-intercepts of the function f(x) = 4(5((1(-3|x - 1| + 3) - 3)/(-2(-3|x - 1| + 3) + 3))^2 - 3((1(-3|x - 1| + 3) - 3)/(-2(-3|x - 1| + 3) + 3)) - 5) - 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 -3|(2((-3(2e^(2x) - 2) - 1)/(1(2e^(2x) - 2) + 3))^2 - 5((-3(2e^(2x) - 2) - 1)/(1(2e^(2x) - 2) + 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": "Find the number of x-intercepts of the function f(x) = -4(-2((3(2|x + 3| + 2) + 1)/(1(2|x + 3| + 2) + 1)) + 4)^2 - 4(-2((3(2|x + 3| + 2) + 1)/(1(2|x + 3| + 2) + 1)) + 4) + 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = -1sin(1\u03c0(2|(2((-2x)/(1x + 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": "106", "dataset": "MATH"} | |
| {"messages": [{"content": "Determine the number of values x in [-10, 10] where f(x) = 1cos(2\u03c0(-1((3x - 3)/(-3x - 3)) - 5)) - 1 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) = 1(2|(-1cos(1\u03c0x) + 1) - 2| - 1) - 3 where -10 \u2264 x \u2264 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) = -2|((-1(1(-5x^2 - 4x + 1)) - 3)/(3(1(-5x^2 - 4x + 1)) + 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 zeros does the function f(x) = (-2(3(1|(-2sin(1\u03c0x + 2)) - 2| - 2) - 1) - 2)/(1(3(1|(-2sin(1\u03c0x + 2)) - 2| - 2) - 1) - 2) 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 solutions does the equation -2sin(3\u03c0((-2(-5(-2|x + 3|)^2 - 4(-2|x + 3|) + 5) + 3)/(-1(-5(-2|x + 3|)^2 - 4(-2|x + 3|) + 5) - 1)) + 3) - 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) = -1(-2(-2|(1sin(3\u03c0x - 2) + 2) - 1| + 3)^2 + 4) - 4 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) = 5(-2|(1e^(-1x) - 3) - 1| + 1) - 3 where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = -1(-1sin(2\u03c0(-1|x + 2| + 2) - 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": "Find the number of x-intercepts of the function f(x) = (1(2|(-1x - 1) - 1| + 1) - 2)/(-3(2|(-1x - 1) - 1| + 1) + 2) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0(-2|(1((1x + 1)/(2x + 1))^2 - 2((1x + 1)/(2x + 1)) + 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": "41", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = -3(-1e^(2(-1|((3x)/(-2x + 3)) + 3| - 1)) + 1) + 3 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "2", "dataset": "MATH"} | |
| {"messages": [{"content": "How many zeros does the function f(x) = (2(-1|(5(-1x^2 - 5x + 5) + 3) + 3| + 3) + 2)/(2(-1|(5(-1x^2 - 5x + 5) + 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) = -3cos(2\u03c0(4(-3|(-3((-2x + 3)/(-3x + 1))^2 - 3((-2x + 3)/(-3x + 1)) + 4) - 2| - 1) + 4) + 2) + 2 have in the interval [-10, 10]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "317", "dataset": "MATH"} | |
| {"messages": [{"content": "How many solutions does the equation -1sin(1\u03c0((-1(3(2x + 1)^2 + 3(2x + 1) - 3))/(1(3(2x + 1)^2 + 3(2x + 1) - 3) + 3)) - 1) - 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": "Find the number of x-intercepts of the function f(x) = 1(-3(1sin(3\u03c0x + 1) + 2) + 1)^2 + 2(-3(1sin(3\u03c0x + 1) + 2) + 1) where -10 \u2264 x \u2264 10.\n\nPresent the answer in LaTex format: \\boxed{Your answer}", "role": "user"}], "ground_truth": "30", "dataset": "MATH"} | |
| {"messages": [{"content": "How many solutions does the equation -1(-2|(3e^(-2((-3x)/(1x + 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": "8", "dataset": "MATH"} | |
| {"messages": [{"content": "How many solutions does the equation 2sin(2\u03c0(3|(3(-2((-1x - 2)/(-2x - 1)) + 1)^2 - 3(-2((-1x - 2)/(-2x - 1)) + 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": "228", "dataset": "MATH"} | |