VeriEvol: Scaling Multimodal Mathematical Reasoning via Verifiable Evol-Instruct
Paper • 2606.23543 • Published • 6
id string | data_source string | ability string | prompt list | reward_model dict | source dict | extra_info dict | images images list |
|---|---|---|---|---|---|---|---|
244fb109-97f1-4423-92ce-40f0448fabab | MMFineReason_evol | math | [
{
"content": "<image> As shown in the figure, in trapezoid $$ABCD$$, where $$AB \\parallel CD$$, and the ratio of the parallel side lengths is $$AB:CD = 2:1$$. If $$AC$$ intersects $$DB$$ at point $$O$$, calculate the ratio of the area of triangle $$\\triangle AOD$$ to the total area of the trapezoid $$ABCD$$. ... | {
"ground_truth": "\\frac{2}{9}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{2}{9}",
"question": "<image> As shown in the figure, in trapezoid $$ABCD$$, where $$AB \\parallel CD$$, and the ratio of the parallel side lengths is $$AB:CD = 2:1$$. If $$AC$$ intersects $$DB$$ at point $$O$$, calculate the ratio of the area of triangle $$\\triangle AOD$$ to the total area of t... | |
71348c08-c1ba-444d-b0b6-5856a5a20682 | MMFineReason_evol | math | [
{
"content": "<image> Assuming the visual evidence strongly suggests the figure is a perfect square, what is the precise ratio of the length of any single side to the length of its diagonal? You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning pro... | {
"ground_truth": "\\frac{\\sqrt{2}}{2}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{\\sqrt{2}}{2}",
"question": "<image> Assuming the visual evidence strongly suggests the figure is a perfect square, what is the precise ratio of the length of any single side to the length of its diagonal?",
"index": 1,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instru... | |
5cb25d45-a3f2-4c02-b4af-9eb085bd3448 | MMFineReason_evol | math | [
{
"content": "<image> Assuming the linear patterns derived from the tabulated values for $(2x-1)$ and $(x+2)$ continue for positive integer values of $x$, determine the exact value of $x$ for which the quantity $(2x-1)$ is precisely 14 units greater than the quantity $(x+2)$. You FIRST think about the reasoning... | {
"ground_truth": "17",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "17",
"question": "<image> Assuming the linear patterns derived from the tabulated values for $(2x-1)$ and $(x+2)$ continue for positive integer values of $x$, determine the exact value of $x$ for which the quantity $(2x-1)$ is precisely 14 units greater than the quantity $(x+2)$.",
"index": 2,
"spl... | |
8d7aa529-dd41-4f31-866a-3235069839c2 | MMFineReason_evol | math | [
{
"content": "<image> If $S(x_s, y_s)$ is the solution point determined by the intersection of the two graphed lines, $A$ is the $y$-intercept of the line $2x+y=4$, and $B$ is the $x$-intercept of the line $x-y=-1$, what is the precise numerical value of the square of the Euclidean distance between points $A$ a... | {
"ground_truth": "17",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "17",
"question": "<image> If $S(x_s, y_s)$ is the solution point determined by the intersection of the two graphed lines, $A$ is the $y$-intercept of the line $2x+y=4$, and $B$ is the $x$-intercept of the line $x-y=-1$, what is the precise numerical value of the square of the Euclidean distance between... | |
fb736114-5067-4da9-b361-38d5ac5e9230 | MMFineReason_evol | math | [
{
"content": "<image> Assuming the depicted figure is a parallelepiped, calculate the exact quotient resulting from dividing the total number of edges (E) by the difference between the total number of vertices (V) and the number of lateral faces (L). You FIRST think about the reasoning process as an internal mo... | {
"ground_truth": "3",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "3",
"question": "<image> Assuming the depicted figure is a parallelepiped, calculate the exact quotient resulting from dividing the total number of edges (E) by the difference between the total number of vertices (V) and the number of lateral faces (L).",
"index": 4,
"split": "train",
"task": "{\... | |
85cf849d-9788-4b60-b251-f9a97812f724 | MMFineReason_evol | math | [
{
"content": "<image> Given that two squares, each having a side length of $$2$$ cm, are combined exactly as shown to form the resulting large rectangle. Calculate the difference between the sum of the perimeters of the two squares when considered separately and the perimeter of the final, single, combined rect... | {
"ground_truth": "4",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "4",
"question": "<image> Given that two squares, each having a side length of $$2$$ cm, are combined exactly as shown to form the resulting large rectangle. Calculate the difference between the sum of the perimeters of the two squares when considered separately and the perimeter of the final, single, c... | |
9a4332dc-70e8-4667-8566-8514dd68e033 | MMFineReason_evol | math | [
{
"content": "<image> In trapezoid QRTU, V and S are the midpoints of the legs. If the length of the top base RQ is defined by the expression $x+3$, the length of the bottom base UT is defined by $3x-1$, and the length of the midsegment VS is defined by $x+8$, what is the numerical length of the segment UT? You... | {
"ground_truth": "20",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "20",
"question": "<image> In trapezoid QRTU, V and S are the midpoints of the legs. If the length of the top base RQ is defined by the expression $x+3$, the length of the bottom base UT is defined by $3x-1$, and the length of the midsegment VS is defined by $x+8$, what is the numerical length of the se... | |
dae6a95f-537b-49af-8586-59fea6f59799 | MMFineReason_evol | math | [
{
"content": "<image> Given that the ratio of students from regions A, B, and C is 2:7:3, calculate the positive difference, in degrees, between the central angle of the largest sector and the central angle of the medium-sized sector shown in the pie chart. You FIRST think about the reasoning process as an inte... | {
"ground_truth": "120",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "120",
"question": "<image> Given that the ratio of students from regions A, B, and C is 2:7:3, calculate the positive difference, in degrees, between the central angle of the largest sector and the central angle of the medium-sized sector shown in the pie chart.",
"index": 7,
"split": "train",
"t... | |
328694c2-0bd2-4bce-91c6-2240ec08fd28 | MMFineReason_evol | math | [
{
"content": "<image> Assuming the parallelogram's area is 2000 square units, calculate the perimeter of a hypothetical rectangle constructed using the parallelogram's base $(x+10)$ and its height $(x)$ as its two side lengths. You FIRST think about the reasoning process as an internal monologue and then provid... | {
"ground_truth": "180",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "180",
"question": "<image> Assuming the parallelogram's area is 2000 square units, calculate the perimeter of a hypothetical rectangle constructed using the parallelogram's base $(x+10)$ and its height $(x)$ as its two side lengths.",
"index": 8,
"split": "train",
"task": "{\"domain\": [\"Math\"]... | |
69991729-82c0-4ba5-b7e1-9ae57da88dde | MMFineReason_evol | math | [
{
"content": "<image> Assuming that the two-dimensional figure labeled C is perfectly constructed to form a right circular cylinder, what is the exact mathematical ratio of the length of the central rectangle (the dimension that wraps around the circular base) to the diameter of one of the circular bases? You F... | {
"ground_truth": "\\pi",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\pi",
"question": "<image> Assuming that the two-dimensional figure labeled C is perfectly constructed to form a right circular cylinder, what is the exact mathematical ratio of the length of the central rectangle (the dimension that wraps around the circular base) to the diameter of one of the circul... | |
83641707-a7a5-4bf5-b347-ad32b74f423b | MMFineReason_evol | math | [
{
"content": "<image> Given that points $D$ and $E$ are the midpoints of sides $AB$ and $AC$ in $\triangle ABC$, respectively, and the area of the trapezoid $DBCE$ is $27 \\text{ cm}^2$, what is the area of $\\triangle ADE$ in $\\text{cm}^2$? You FIRST think about the reasoning process as an internal monologue ... | {
"ground_truth": "9",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "9",
"question": "<image> Given that points $D$ and $E$ are the midpoints of sides $AB$ and $AC$ in $\triangle ABC$, respectively, and the area of the trapezoid $DBCE$ is $27 \\text{ cm}^2$, what is the area of $\\triangle ADE$ in $\\text{cm}^2$?",
"index": 10,
"split": "train",
"task": "{\"domain... | |
425b86fc-3a60-49a1-b9f8-e1845f4e9f6f | MMFineReason_evol | math | [
{
"content": "<image> What is the exact volume of the region inside the cube that is not occupied by the inscribed sphere? You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer... | {
"ground_truth": "64 - \\frac{32}{3}\\pi",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "64 - \\frac{32}{3}\\pi",
"question": "<image> What is the exact volume of the region inside the cube that is not occupied by the inscribed sphere?",
"index": 11,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
} | |
ef18b388-cf2d-42ab-acbd-09e7202d9e3a | MMFineReason_evol | math | [
{
"content": "<image> Given the visual information that the distance from the sphere's center to the cutting plane is $h=3$, and provided the sphere has a radius of $R=5$, determine the ratio of the area of the circular cross-section ($A_{cross}$) to the total surface area of the sphere ($A_{sphere}$). Express ... | {
"ground_truth": "4/25",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "4/25",
"question": "<image> Given the visual information that the distance from the sphere's center to the cutting plane is $h=3$, and provided the sphere has a radius of $R=5$, determine the ratio of the area of the circular cross-section ($A_{cross}$) to the total surface area of the sphere ($A_{sphe... | |
01247d9a-75cb-4954-80e5-c8f5078fffbb | MMFineReason_evol | math | [
{
"content": "<image> The diagram illustrates a coreless high-frequency induction furnace, where the alternating current in the coil induces eddy currents within the molten metal. The interaction between these induced currents and the alternating magnetic field generates a substantial Lorentz force on the mater... | {
"ground_truth": "C",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "C",
"question": "<image> The diagram illustrates a coreless high-frequency induction furnace, where the alternating current in the coil induces eddy currents within the molten metal. The interaction between these induced currents and the alternating magnetic field generates a substantial Lorentz force ... | |
c8cb6129-0537-4ec8-82fe-a002afd3565f | MMFineReason_evol | math | [
{
"content": "<image> In the figure, in $$\triangle ABC$$, $$DE \\parallel BC$$, $$AE = 2$$, $$EC = 3$$. If $S_{\\triangle ADE}$ is the area of $\\triangle ADE$ and $S_{DBCE}$ is the area of the quadrilateral $DBCE$, what is the exact value of the ratio $S_{\\triangle ADE} : S_{DBCE}$? You FIRST think about the... | {
"ground_truth": "\\frac{4}{21}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{4}{21}",
"question": "<image> In the figure, in $$\triangle ABC$$, $$DE \\parallel BC$$, $$AE = 2$$, $$EC = 3$$. If $S_{\\triangle ADE}$ is the area of $\\triangle ADE$ and $S_{DBCE}$ is the area of the quadrilateral $DBCE$, what is the exact value of the ratio $S_{\\triangle ADE} : S_{DBCE}$?",... | |
0e9daea9-0d25-4833-9a70-8908f1a95819 | MMFineReason_evol | math | [
{
"content": "<image> As shown in the figure, in $$\\triangle ABC$$, $$DE$$ ∥ $$BC$$. If $$AD=3$$, $$DB=5$$, and $$DE=3.3$$, what is the ratio of the area of the trapezoid $$DBCE$$ to the area of $$\\triangle ADE$$? You FIRST think about the reasoning process as an internal monologue and then provide the final ... | {
"ground_truth": "\\frac{55}{9}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{55}{9}",
"question": "<image> As shown in the figure, in $$\\triangle ABC$$, $$DE$$ ∥ $$BC$$. If $$AD=3$$, $$DB=5$$, and $$DE=3.3$$, what is the ratio of the area of the trapezoid $$DBCE$$ to the area of $$\\triangle ADE$$?",
"index": 15,
"split": "train",
"task": "{\"domain\": [\"Math\"],... | |
ce2407b7-110d-43e9-a328-3b4cc33b47e8 | MMFineReason_evol | math | [
{
"content": "<image> As shown in the figure, ⊙O is the circumcircle of △ABC. Given that ∠OAB = 30°, and the length of chord BC is equal to the length of chord AB, what is the measure of the inscribed angle ∠CAB? You FIRST think about the reasoning process as an internal monologue and then provide the final ans... | {
"ground_truth": "60°",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "60°",
"question": "<image> As shown in the figure, ⊙O is the circumcircle of △ABC. Given that ∠OAB = 30°, and the length of chord BC is equal to the length of chord AB, what is the measure of the inscribed angle ∠CAB?",
"index": 16,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"... | |
69b2161a-6b0b-4864-89b4-0e467f85d957 | MMFineReason_evol | math | [
{
"content": "<image> In the figure, BD is the altitude from B to side AC of △ABC. Given that ∠A = 55° and ∠C = 65°, what is the numerical ratio of the measure of ∠ABD to the measure of ∠DBC, expressed in simplest fractional form (e.g., 5/3)? You FIRST think about the reasoning process as an internal monologue ... | {
"ground_truth": "7/5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "7/5",
"question": "<image> In the figure, BD is the altitude from B to side AC of △ABC. Given that ∠A = 55° and ∠C = 65°, what is the numerical ratio of the measure of ∠ABD to the measure of ∠DBC, expressed in simplest fractional form (e.g., 5/3)?",
"index": 17,
"split": "train",
"task": "{\"doma... | |
cc9c9ff4-9e51-4d0c-b9b9-2459fa64a122 | MMFineReason_evol | math | [
{
"content": "<image> In $\\triangle ABC$, $AB=8$, points $D$ and $E$ are the midpoints of $BC$ and $CA$ respectively. If $AC=12$ and the perimeter of $\\triangle ABC$ is 30, let $F$ be the midpoint of $AB$. What is the perimeter of the triangle formed by connecting the midpoints, $\\triangle DEF$? You FIRST th... | {
"ground_truth": "15",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "15",
"question": "<image> In $\\triangle ABC$, $AB=8$, points $D$ and $E$ are the midpoints of $BC$ and $CA$ respectively. If $AC=12$ and the perimeter of $\\triangle ABC$ is 30, let $F$ be the midpoint of $AB$. What is the perimeter of the triangle formed by connecting the midpoints, $\\triangle DEF$?... | |
203cbfc1-96d1-4346-b5e0-345614fa4f24 | MMFineReason_evol | math | [
{
"content": "<image> Using the dimensions displayed (Length=4, Width=3, Height=5), calculate the ratio of the cuboid's total exterior surface area (in $cm^2$) to the square of the length of its longest internal space diagonal (in $cm^2$). Express the result as a simplified common fraction (e.g., 5/3). The answ... | {
"ground_truth": "47/25",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "47/25",
"question": "<image> Using the dimensions displayed (Length=4, Width=3, Height=5), calculate the ratio of the cuboid's total exterior surface area (in $cm^2$) to the square of the length of its longest internal space diagonal (in $cm^2$). Express the result as a simplified common fraction (e.g.... | |
b153046a-1026-4a5e-9e49-ae6bd412461e | MMFineReason_evol | math | [
{
"content": "<image> Based on the provided initial ball counts (2 white, 4 black, 6 red, $b$ yellow) and the observed frequency for drawing a black ball ($F_B = 0.2$), calculate the precise probability that if two balls are drawn sequentially *without replacement* from the bag, the first ball drawn is Red and ... | {
"ground_truth": "3/95",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "3/95",
"question": "<image> Based on the provided initial ball counts (2 white, 4 black, 6 red, $b$ yellow) and the observed frequency for drawing a black ball ($F_B = 0.2$), calculate the precise probability that if two balls are drawn sequentially *without replacement* from the bag, the first ball dr... | |
8b0b3a2a-effc-4a7a-97fa-367ce748f7e5 | MMFineReason_evol | math | [
{
"content": "<image> Given the probabilities $P(I)=0.15$, $P(II)=0.20$, and $P(III)=0.45$, suppose a scoring system assigns 10 points for a hit in region I, 5 points for a hit in region II, 1 point for a hit in region III, and a penalty of 5 points for missing the target entirely. What is the mathematically ex... | {
"ground_truth": "1.95",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "1.95",
"question": "<image> Given the probabilities $P(I)=0.15$, $P(II)=0.20$, and $P(III)=0.45$, suppose a scoring system assigns 10 points for a hit in region I, 5 points for a hit in region II, 1 point for a hit in region III, and a penalty of 5 points for missing the target entirely. What is the ma... | |
c4d2b5dd-4f75-45fb-8592-a23a4049ce16 | MMFineReason_evol | math | [
{
"content": "<image> If the length of the chord $\\overline{JL}$ is equal to the radius of the circle, determine the measure, in degrees, of the major arc $\\widehat{JKL}$ (the arc traversing from J to L via K). You FIRST think about the reasoning process as an internal monologue and then provide the final ans... | {
"ground_truth": "300°",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "300°",
"question": "<image> If the length of the chord $\\overline{JL}$ is equal to the radius of the circle, determine the measure, in degrees, of the major arc $\\widehat{JKL}$ (the arc traversing from J to L via K).",
"index": 22,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \... | |
64bf898f-fd25-401d-b036-cef84ddebc89 | MMFineReason_evol | math | [
{
"content": "<image> What is the exact perpendicular distance from the point $A(0, 3, 0)$ to the plane $\\alpha: x + y + z = 0$? Express the answer as a simplified radical. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE encl... | {
"ground_truth": "\\sqrt{3}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\sqrt{3}",
"question": "<image> What is the exact perpendicular distance from the point $A(0, 3, 0)$ to the plane $\\alpha: x + y + z = 0$? Express the answer as a simplified radical.",
"index": 23,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
} | |
e148bdf3-56d6-4853-ae68-6b50afdc85dd | MMFineReason_evol | math | [
{
"content": "<image> Calculate the length of the altitude corresponding to the side measuring 13 cm. Round the final answer to the nearest hundredth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </t... | {
"ground_truth": "Approximately 12.64 cm (or exactly 30√30 / 13 cm)",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "Approximately 12.64 cm (or exactly 30√30 / 13 cm)",
"question": "<image> Calculate the length of the altitude corresponding to the side measuring 13 cm. Round the final answer to the nearest hundredth.",
"index": 24,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
... | |
fb9cd876-97fd-4655-aa3d-db4fc6fa6680 | MMFineReason_evol | math | [
{
"content": "<image> Given the conical paper hat shown, where the base radius is $8\\ \\mathrm{cm}$ and the slant height is $25\\ \\mathrm{cm}$, determine the precise measure, in degrees, of the central angle of the circular sector (the net indicated by the dashed lines) required to form the hat's lateral surf... | {
"ground_truth": "115.2",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "115.2",
"question": "<image> Given the conical paper hat shown, where the base radius is $8\\ \\mathrm{cm}$ and the slant height is $25\\ \\mathrm{cm}$, determine the precise measure, in degrees, of the central angle of the circular sector (the net indicated by the dashed lines) required to form the ha... | |
23865855-5475-4475-97cf-85bd85910663 | MMFineReason_evol | math | [
{
"content": "<image> As shown in the figure, a wooden pole standing vertically on the ground breaks at a height of 3m from the ground. If the height of the pole before it broke was 8m, what is the ratio of the area of the resulting right-angled triangle formed by the broken pole structure and the ground to the... | {
"ground_truth": "6/25",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "6/25",
"question": "<image> As shown in the figure, a wooden pole standing vertically on the ground breaks at a height of 3m from the ground. If the height of the pole before it broke was 8m, what is the ratio of the area of the resulting right-angled triangle formed by the broken pole structure and th... | |
6fcf60f8-1ce3-47f7-af73-79fdb81448db | MMFineReason_evol | math | [
{
"content": "<image> Given that the rhombus $ABCD$ has diagonals $AC=16$ and $BD=12$, determine the exact rational value of the expression $\frac{(\text{Perimeter of } ABCD)^2}{\text{Area of } ABCD}$. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The re... | {
"ground_truth": "\\frac{50}{3}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{50}{3}",
"question": "<image> Given that the rhombus $ABCD$ has diagonals $AC=16$ and $BD=12$, determine the exact rational value of the expression $\frac{(\text{Perimeter of } ABCD)^2}{\text{Area of } ABCD}$.",
"index": 27,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"i... | |
f99c6fc1-d42a-4f9b-8c66-ab21a4b6ebc2 | MMFineReason_evol | math | [
{
"content": "<image> What is the numerical value of the ratio formed by dividing the square of the distance between the two points where the function $f(x) = x^2 - 4x + 5$ intersects the line $y = -2x + 5$, by the y-coordinate of the parabola's minimum point? You FIRST think about the reasoning process as an i... | {
"ground_truth": "20",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "20",
"question": "<image> What is the numerical value of the ratio formed by dividing the square of the distance between the two points where the function $f(x) = x^2 - 4x + 5$ intersects the line $y = -2x + 5$, by the y-coordinate of the parabola's minimum point?",
"index": 28,
"split": "train",
... | |
352dde70-1b95-42e2-a305-acf65a38bf2b | MMFineReason_evol | math | [
{
"content": "<image> If the quadratic function is given by $y = ax^2 + bx + c$, and the graph passes through point $A(3, 0)$ with an axis of symmetry at $x = 1$, which of the following equations must be satisfied by the coefficients $a, b, \text{ and } c$? You FIRST think about the reasoning process as an inte... | {
"ground_truth": "a - b + c = 0",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "a - b + c = 0",
"question": "<image> If the quadratic function is given by $y = ax^2 + bx + c$, and the graph passes through point $A(3, 0)$ with an axis of symmetry at $x = 1$, which of the following equations must be satisfied by the coefficients $a, b, \text{ and } c$?",
"index": 29,
"split": "t... | |
1ba1e5b3-66cc-43d3-88e6-4eeceb16e590 | MMFineReason_evol | math | [
{
"content": "<image> In this oblique coordinate system $xOy$, given $\\overrightarrow{a} = \\langle 2, 3 \\rangle$ and $\\overrightarrow{b} = \\langle -5, 2 \\rangle$, determine the scalar $k$ such that the vector $\\overrightarrow{v} = k \\overrightarrow{a} + \\overrightarrow{b}$ is orthogonal to $\\overright... | {
"ground_truth": "4/13",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "4/13",
"question": "<image> In this oblique coordinate system $xOy$, given $\\overrightarrow{a} = \\langle 2, 3 \\rangle$ and $\\overrightarrow{b} = \\langle -5, 2 \\rangle$, determine the scalar $k$ such that the vector $\\overrightarrow{v} = k \\overrightarrow{a} + \\overrightarrow{b}$ is orthogonal ... | |
3a569c4f-97c5-4429-a39e-8806d81680fb | MMFineReason_evol | math | [
{
"content": "<image> If the total volume of the solid figure must remain constant, and the height of the rectangular prism base is reduced from 6 m to 5 m, by what percentage must the 10 m length increase to maintain the original volume? Round your answer to two decimal places. You FIRST think about the reason... | {
"ground_truth": "15.38%",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "15.38%",
"question": "<image> If the total volume of the solid figure must remain constant, and the height of the rectangular prism base is reduced from 6 m to 5 m, by what percentage must the 10 m length increase to maintain the original volume? Round your answer to two decimal places.",
"index": 31... | |
ff609c10-1581-47b0-ac10-1e31017dacd5 | MMFineReason_evol | math | [
{
"content": "<image> In the figure, given that △ABC has ∠C = 90°, AC = 3, and AB = 5. If CD is the altitude drawn from C to the hypotenuse AB, calculate the exact length of the segment BD. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning proc... | {
"ground_truth": "16/5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "16/5",
"question": "<image> In the figure, given that △ABC has ∠C = 90°, AC = 3, and AB = 5. If CD is the altitude drawn from C to the hypotenuse AB, calculate the exact length of the segment BD.",
"index": 32,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
} | |
3a2ac2cd-da91-4516-8736-dfb9a3cd0012 | MMFineReason_evol | math | [
{
"content": "<image> In rectangle $$ABCD$$, diagonals $$AC$$ and $$BD$$ intersect at point $$O$$. If $$\\angle AOB=60^{\\circ}$$ and $$AC=10$$, what is the exact area of the rectangle $$ABCD$$? You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning... | {
"ground_truth": "25\\sqrt{3}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "25\\sqrt{3}",
"question": "<image> In rectangle $$ABCD$$, diagonals $$AC$$ and $$BD$$ intersect at point $$O$$. If $$\\angle AOB=60^{\\circ}$$ and $$AC=10$$, what is the exact area of the rectangle $$ABCD$$?",
"index": 33,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instructio... | |
175d7e8c-a281-416e-b9c2-9ddaf3b3b82c | MMFineReason_evol | math | [
{
"content": "<image> If the parameters $a$ and $b$ derived from the given system of inequalities and its combined solution set define the linear coefficient $-(a+b)$ of a new quadratic inequality $x^2 - (a+b)x + c < 0$, and the solution set for this new inequality is the open interval $(-1, 5)$, what is the co... | {
"ground_truth": "-5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "-5",
"question": "<image> If the parameters $a$ and $b$ derived from the given system of inequalities and its combined solution set define the linear coefficient $-(a+b)$ of a new quadratic inequality $x^2 - (a+b)x + c < 0$, and the solution set for this new inequality is the open interval $(-1, 5)$, w... | |
d06e1fe0-70f9-4a1a-854c-04e0aba207c7 | MMFineReason_evol | math | [
{
"content": "<image> Assuming the figure is a rhombus, calculate the total area of the quadrilateral. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE put in \\\\... | {
"ground_truth": "216",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "216",
"question": "<image> Assuming the figure is a rhombus, calculate the total area of the quadrilateral.",
"index": 35,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
} | |
d0edc71d-d86f-4956-9eda-6332b929a3e9 | MMFineReason_evol | math | [
{
"content": "<image> Given that the area of the sector in the lateral surface development of a cone is 65π cm², and the arc length of the sector is 10π cm, calculate the volume of the resulting cone in terms of π (cm³). You FIRST think about the reasoning process as an internal monologue and then provide the f... | {
"ground_truth": "100\\pi",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "100\\pi",
"question": "<image> Given that the area of the sector in the lateral surface development of a cone is 65π cm², and the arc length of the sector is 10π cm, calculate the volume of the resulting cone in terms of π (cm³).",
"index": 36,
"split": "train",
"task": "{\"domain\": [\"Math\"], ... | |
a635310f-bf91-40d1-8e4a-ad083877f4da | MMFineReason_evol | math | [
{
"content": "<image> If an instruction $a \\leftarrow b$ were inserted immediately after the statement $b \\leftarrow 5$, and the final print statement were modified to $\\text{Print } (2a - b)$, what numerical value would be displayed? You FIRST think about the reasoning process as an internal monologue and t... | {
"ground_truth": "5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "5",
"question": "<image> If an instruction $a \\leftarrow b$ were inserted immediately after the statement $b \\leftarrow 5$, and the final print statement were modified to $\\text{Print } (2a - b)$, what numerical value would be displayed?",
"index": 37,
"split": "train",
"task": "{\"domain\": [... | |
713a812e-fd6b-4b3e-8974-2ae00744c0c4 | MMFineReason_evol | math | [
{
"content": "<image> Given the total class size of 48 students and the pocket money frequency distribution shown, where the height ratio of the bars corresponding to the spending intervals [2, 4), [4, 6), [6, 8), [8, 10), and [10, 12] yuan is 2:3:4:2:1 respectively, what is the calculated average (mean) pocket... | {
"ground_truth": "6.5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "6.5",
"question": "<image> Given the total class size of 48 students and the pocket money frequency distribution shown, where the height ratio of the bars corresponding to the spending intervals [2, 4), [4, 6), [6, 8), [8, 10), and [10, 12] yuan is 2:3:4:2:1 respectively, what is the calculated average... | |
547259e5-a7c9-48b4-8bbc-d6760699e127 | MMFineReason_evol | math | [
{
"content": "<image> In the right triangle $ABC$, $\\angle C=90\\degree$, $AB=5$, and $BC=4$. If $CD$ is the altitude drawn from vertex $C$ to the hypotenuse $AB$, what is the exact value of the ratio $\\frac{CD}{AD}$? (Express the answer as a simplified fraction.) You FIRST think about the reasoning process a... | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{4}{3}",
"question": "<image> In the right triangle $ABC$, $\\angle C=90\\degree$, $AB=5$, and $BC=4$. If $CD$ is the altitude drawn from vertex $C$ to the hypotenuse $AB$, what is the exact value of the ratio $\\frac{CD}{AD}$? (Express the answer as a simplified fraction.)",
"index": 39,
"sp... | |
78923f32-5791-44fe-90a7-0ca97def6153 | MMFineReason_evol | math | [
{
"content": "<image> If the skier and equipment have a combined mass of $$80\\ \\unit{kg}$$ and start from rest at point A, what is the kinetic energy (in Joules) of the skier upon reaching point B, assuming the path is perfectly frictionless? (Use $$g = 9.8\\ \\unit{m/s^2}$$ for the acceleration due to gravit... | {
"ground_truth": "219520",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "219520",
"question": "<image> If the skier and equipment have a combined mass of $$80\\ \\unit{kg}$$ and start from rest at point A, what is the kinetic energy (in Joules) of the skier upon reaching point B, assuming the path is perfectly frictionless? (Use $$g = 9.8\\ \\unit{m/s^2}$$ for the accelerat... | |
19d3dbb4-c1ec-487f-a51b-f6ae259238d6 | MMFineReason_evol | math | [
{
"content": "<image> If the assignment statement in the first rectangular box ($m \\leftarrow 1$) were replaced by $m \\leftarrow 5$, and the instruction in the second rectangular box ($p \\leftarrow m+2$) were simultaneously replaced by $p \\leftarrow 2m + 1$, what numerical value would the program output for... | {
"ground_truth": "14",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "14",
"question": "<image> If the assignment statement in the first rectangular box ($m \\leftarrow 1$) were replaced by $m \\leftarrow 5$, and the instruction in the second rectangular box ($p \\leftarrow m+2$) were simultaneously replaced by $p \\leftarrow 2m + 1$, what numerical value would the progr... | |
1cc75ea3-1233-47d2-9601-3d61e0f85487 | MMFineReason_evol | math | [
{
"content": "<image> Based on the dimensions derived from the given information ($A_{base}=\\pi, h=1$), calculate the cylinder's total surface area (including both top and bottom caps). If a sphere (S) is constructed such that its surface area is numerically equal to this cylinder's total surface area, what is... | {
"ground_truth": "\\frac{4}{3}\\pi",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{4}{3}\\pi",
"question": "<image> Based on the dimensions derived from the given information ($A_{base}=\\pi, h=1$), calculate the cylinder's total surface area (including both top and bottom caps). If a sphere (S) is constructed such that its surface area is numerically equal to this cylinder's ... | |
b9a45d52-adf2-4a8f-9102-727251cc316a | MMFineReason_evol | math | [
{
"content": "<image> If the height AO is maintained as the square root of 3 times the radius OB, and the slant height AB is measured to be 12 units, what is the numerical coefficient of π in the cone's total surface area? You FIRST think about the reasoning process as an internal monologue and then provide the... | {
"ground_truth": "108",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "108",
"question": "<image> If the height AO is maintained as the square root of 3 times the radius OB, and the slant height AB is measured to be 12 units, what is the numerical coefficient of π in the cone's total surface area?",
"index": 43,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"... | |
6c042992-58c1-4dbc-a48c-d0b5440ceb48 | MMFineReason_evol | math | [
{
"content": "<image> If the four small squares, each with a perimeter of 4 cm (as shown in the figure), were rearranged to form the largest possible square, by what factor is the perimeter of the shown 1x4 rectangle greater than the perimeter of the resulting large square? Express the answer as a simplified fr... | {
"ground_truth": "5/4",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "5/4",
"question": "<image> If the four small squares, each with a perimeter of 4 cm (as shown in the figure), were rearranged to form the largest possible square, by what factor is the perimeter of the shown 1x4 rectangle greater than the perimeter of the resulting large square? Express the answer as a... | |
4343d557-afc9-4c63-ab97-46361b95be76 | MMFineReason_evol | math | [
{
"content": "<image> The points C and D are established as the midpoints of segments OA and OB respectively. If the measured length of the segment CD is 20m, and the total accessible length of the two sides $OA + OB$ is 120 meters, what is the exact perimeter (in meters) of the trapezoidal region $ABDC$? You F... | {
"ground_truth": "120",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "120",
"question": "<image> The points C and D are established as the midpoints of segments OA and OB respectively. If the measured length of the segment CD is 20m, and the total accessible length of the two sides $OA + OB$ is 120 meters, what is the exact perimeter (in meters) of the trapezoidal region... | |
b1ec34db-bcab-4229-984c-bbf76fa0a4f3 | MMFineReason_evol | math | [
{
"content": "<image> As shown in the figure, $ABCD$ is a rhombus with diagonals $AC$ and $BD$ intersecting at point $O$. Given that the sum of the lengths of the diagonals is $AC + BD = 28$ and the area of the rhombus is 96. If $E$ is the midpoint of $AB$, what is the length of $OE$? You FIRST think about the ... | {
"ground_truth": "5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "5",
"question": "<image> As shown in the figure, $ABCD$ is a rhombus with diagonals $AC$ and $BD$ intersecting at point $O$. Given that the sum of the lengths of the diagonals is $AC + BD = 28$ and the area of the rhombus is 96. If $E$ is the midpoint of $AB$, what is the length of $OE$?",
"index": 4... | |
e3581cef-c8ff-4ed5-b563-1d3e2bfd4899 | MMFineReason_evol | math | [
{
"content": "<image> Given the figure where $AB\\perp BC$, and the degree of $\\angle ABD$ is $15^\\circ$ less than twice the degree of $\\angle DBC$. If ray $BF$ is constructed such that it bisects $\\angle ABD$, and ray $BG$ is constructed such that it bisects $\\angle DBC$, what is the precise numerical mea... | {
"ground_truth": "45",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "45",
"question": "<image> Given the figure where $AB\\perp BC$, and the degree of $\\angle ABD$ is $15^\\circ$ less than twice the degree of $\\angle DBC$. If ray $BF$ is constructed such that it bisects $\\angle ABD$, and ray $BG$ is constructed such that it bisects $\\angle DBC$, what is the precise ... | |
d402d648-4814-4c53-8d42-e4a45849160a | MMFineReason_evol | math | [
{
"content": "<image> A right circular cylinder is constructed such that both its radius and its height are exactly equal to the radius ($r=3$) of the depicted hemisphere. What is the exact numerical ratio of the volume of the hemisphere to the lateral surface area of this newly constructed cylinder? You FIRST ... | {
"ground_truth": "1",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "1",
"question": "<image> A right circular cylinder is constructed such that both its radius and its height are exactly equal to the radius ($r=3$) of the depicted hemisphere. What is the exact numerical ratio of the volume of the hemisphere to the lateral surface area of this newly constructed cylinder... | |
d71999af-ef16-4d54-8f52-8f6fbc476441 | MMFineReason_evol | math | [
{
"content": "<image> If the initial variable assignment box $m=2$ were hypothetically replaced by $m=4$, and the subsequent calculation box $n=p+5$ were replaced by $n=2p$, what would be the resulting output value for $n$? You FIRST think about the reasoning process as an internal monologue and then provide th... | {
"ground_truth": "14",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "14",
"question": "<image> If the initial variable assignment box $m=2$ were hypothetically replaced by $m=4$, and the subsequent calculation box $n=p+5$ were replaced by $n=2p$, what would be the resulting output value for $n$?",
"index": 49,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"... | |
dc7c51f0-ff98-4ad3-b66b-45d23a040aef | MMFineReason_evol | math | [
{
"content": "<image> Based on the input parameters a and b, the program calculates the volume V. If the height 'b' were doubled, but the volume 'V' remained exactly the same, what would be the precise value of the square of the new base edge length 'a'? You FIRST think about the reasoning process as an interna... | {
"ground_truth": "2",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "2",
"question": "<image> Based on the input parameters a and b, the program calculates the volume V. If the height 'b' were doubled, but the volume 'V' remained exactly the same, what would be the precise value of the square of the new base edge length 'a'?",
"index": 50,
"split": "train",
"task"... | |
4498372d-8a55-4d64-8c9d-fe387c09bdcd | MMFineReason_evol | math | [
{
"content": "<image> Assume the cube shown has a side length $s$. If the numerical volume of the cube is equal to the numerical product of the length of a face diagonal (like segment $x$ or $y$) and the length of a space diagonal (a segment connecting two opposite vertices through the cube's interior), what is... | {
"ground_truth": "2√3",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "2√3",
"question": "<image> Assume the cube shown has a side length $s$. If the numerical volume of the cube is equal to the numerical product of the length of a face diagonal (like segment $x$ or $y$) and the length of a space diagonal (a segment connecting two opposite vertices through the cube's inte... | |
1d54f687-b8f1-4dd6-b0e8-7fb94494cedf | MMFineReason_evol | math | [
{
"content": "<image> Let $m_{abs}$ be the absolute value of the slope of the linear function that passes through the origin ($y=-x$), and $c_{int}$ be the y-intercept of the linear function that does not pass through the origin ($y=2x+1$). Determine the positive value $x_k$ such that the instantaneous rate of ... | {
"ground_truth": "\\frac{1}{3}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{1}{3}",
"question": "<image> Let $m_{abs}$ be the absolute value of the slope of the linear function that passes through the origin ($y=-x$), and $c_{int}$ be the y-intercept of the linear function that does not pass through the origin ($y=2x+1$). Determine the positive value $x_k$ such that the... | |
f77d9d39-8792-4326-b41d-1441facb4dd1 | MMFineReason_evol | math | [
{
"content": "<image> In 2019, 50 acres were planted according to the figure (A: 60%, B: 30%, C: 10%). The base expands the total area in 2020, keeping the area of variety B unchanged, resulting in variety B constituting 10% of the new total planting area. If the newly added planting area for variety A is const... | {
"ground_truth": "70\\%",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "70\\%",
"question": "<image> In 2019, 50 acres were planted according to the figure (A: 60%, B: 30%, C: 10%). The base expands the total area in 2020, keeping the area of variety B unchanged, resulting in variety B constituting 10% of the new total planting area. If the newly added planting area for va... | |
f75763f6-f421-481e-adf2-b7955db6a691 | MMFineReason_evol | math | [
{
"content": "<image> If the input $R$ represents the area of a square, and the output $a$ represents the length of the diagonal of that same square, determine the perimeter of a separate square whose area is numerically equivalent to the calculated value of $a$, given the initial input $R=18$. You FIRST think ... | {
"ground_truth": "4\\sqrt{6}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "4\\sqrt{6}",
"question": "<image> If the input $R$ represents the area of a square, and the output $a$ represents the length of the diagonal of that same square, determine the perimeter of a separate square whose area is numerically equivalent to the calculated value of $a$, given the initial input $R=... | |
55619ff5-f69f-4b78-9d7f-d866989f8932 | MMFineReason_evol | math | [
{
"content": "<image> Given that Prism A is a right prism with height $h=6$, and Prism B is an oblique prism: if the area of the trapezoidal base of Prism B is exactly twice the area of the triangular base of Prism A, and the perpendicular height of Prism B is $2/3$ the height of Prism A, calculate the ratio of... | {
"ground_truth": "4/3",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "4/3",
"question": "<image> Given that Prism A is a right prism with height $h=6$, and Prism B is an oblique prism: if the area of the trapezoidal base of Prism B is exactly twice the area of the triangular base of Prism A, and the perpendicular height of Prism B is $2/3$ the height of Prism A, calculat... | |
25da29a3-8d94-4fd0-b2a5-8587b429ecd1 | MMFineReason_evol | math | [
{
"content": "<image> Based on the provided three-view drawings, if the geometric solid has a height ($h$) such that the ratio of its height to its base radius ($r$) is $h:r = \\sqrt{3}:1$, what is the measure (in degrees) of the central angle of the circular sector created when the lateral surface of the solid... | {
"ground_truth": "180",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "180",
"question": "<image> Based on the provided three-view drawings, if the geometric solid has a height ($h$) such that the ratio of its height to its base radius ($r$) is $h:r = \\sqrt{3}:1$, what is the measure (in degrees) of the central angle of the circular sector created when the lateral surfac... | |
16e260ec-679d-439a-9494-a48324f1994c | MMFineReason_evol | math | [
{
"content": "<image> Given the parabola $y=ax^2+bx+c$ shown, which has an axis of symmetry at $x=2$ and an x-intercept at $(5, 0)$, if the y-intercept $c$ is numerically equal to $-5$, what is the exact value of the quantity $4a + 2b + c$? You FIRST think about the reasoning process as an internal monologue an... | {
"ground_truth": "-9",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "-9",
"question": "<image> Given the parabola $y=ax^2+bx+c$ shown, which has an axis of symmetry at $x=2$ and an x-intercept at $(5, 0)$, if the y-intercept $c$ is numerically equal to $-5$, what is the exact value of the quantity $4a + 2b + c$?",
"index": 57,
"split": "train",
"task": "{\"domain\... | |
8629d809-f0c9-4a29-b670-8e35a4705c80 | MMFineReason_evol | math | [
{
"content": "<image> Assume the two triangular bases shown in the diagram are equilateral triangles, and the three central rectangular sections are identical. If the edge length of the triangular bases is 4 units and the resulting height of the prism (when folded) is 5 units, what is the exact volume (in cubic... | {
"ground_truth": "20\\sqrt{3}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "20\\sqrt{3}",
"question": "<image> Assume the two triangular bases shown in the diagram are equilateral triangles, and the three central rectangular sections are identical. If the edge length of the triangular bases is 4 units and the resulting height of the prism (when folded) is 5 units, what is the ... | |
fe9c131e-51b7-4e3c-81d3-f8596aedb840 | MMFineReason_evol | math | [
{
"content": "<image> In the figure, given $\\triangle ABC$ with $\\angle ACB = 90^{\\circ}$, $\\angle B = 30^{\\circ}$, $CD$ is the altitude to $AB$, and $AB = 4$. Determine the exact numerical ratio of the area of $\\triangle ADC$ to the area of $\\triangle CDB$. You FIRST think about the reasoning process as... | {
"ground_truth": "1/3",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "1/3",
"question": "<image> In the figure, given $\\triangle ABC$ with $\\angle ACB = 90^{\\circ}$, $\\angle B = 30^{\\circ}$, $CD$ is the altitude to $AB$, and $AB = 4$. Determine the exact numerical ratio of the area of $\\triangle ADC$ to the area of $\\triangle CDB$.",
"index": 59,
"split": "tra... | |
a791575c-96ec-43f7-9978-05c42cb6dc3c | MMFineReason_evol | math | [
{
"content": "<image> As shown in the figure, points A, C, and B are collinear, and $\\angle 1 = 4\\angle 2$. If a ray CE is drawn such that E lies in the interior of $\\angle ACD$ ($\\angle 1$) and $\\angle ACE$ measures exactly one-third of $\\angle 1$, what is the degree measure of $\\angle DCE$? You FIRST t... | {
"ground_truth": "96^\\circ",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "96^\\circ",
"question": "<image> As shown in the figure, points A, C, and B are collinear, and $\\angle 1 = 4\\angle 2$. If a ray CE is drawn such that E lies in the interior of $\\angle ACD$ ($\\angle 1$) and $\\angle ACE$ measures exactly one-third of $\\angle 1$, what is the degree measure of $\\ang... | |
da95a2c7-6333-4e87-9214-543e9270631e | MMFineReason_evol | math | [
{
"content": "<image> Assuming the figure is an ideal geometric representation of the solid type it depicts, calculate the quotient obtained by dividing the total number of faces that are defined as parallelograms by the total number of edges in the figure. You FIRST think about the reasoning process as an inte... | {
"ground_truth": "0.5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "0.5",
"question": "<image> Assuming the figure is an ideal geometric representation of the solid type it depicts, calculate the quotient obtained by dividing the total number of faces that are defined as parallelograms by the total number of edges in the figure.",
"index": 61,
"split": "train",
"... | |
fbd7618b-2f15-4e69-9024-62155ba6563e | MMFineReason_evol | math | [
{
"content": "<image> In $\\triangle ABC$, $AE$ is the angle bisector, $\\angle B=52^{\\circ}$, and $\\angle C=72^{\\circ}$. If $AD$ is the altitude constructed from vertex $A$ to side $BC$ ($D$ lies on $BC$), what is the measure of the angle $\\angle DAE$ in degrees? You FIRST think about the reasoning process... | {
"ground_truth": "10",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "10",
"question": "<image> In $\\triangle ABC$, $AE$ is the angle bisector, $\\angle B=52^{\\circ}$, and $\\angle C=72^{\\circ}$. If $AD$ is the altitude constructed from vertex $A$ to side $BC$ ($D$ lies on $BC$), what is the measure of the angle $\\angle DAE$ in degrees?",
"index": 62,
"split": "t... | |
1becdee6-a06a-4a09-90ea-b3c4ccc185ab | MMFineReason_evol | math | [
{
"content": "<image> The flight height $h$ (meters) of the struck ball and the flight time $t$ (seconds) are related by $h=20t-5t^2$. Using this relationship to determine the total flight time and the initial vertical velocity component, and further assuming, based on the visual representation of the launch ve... | {
"ground_truth": "139",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "139",
"question": "<image> The flight height $h$ (meters) of the struck ball and the flight time $t$ (seconds) are related by $h=20t-5t^2$. Using this relationship to determine the total flight time and the initial vertical velocity component, and further assuming, based on the visual representation of... | |
1eeafbee-f57f-45ad-bbd2-9cfc930a959f | MMFineReason_evol | math | [
{
"content": "<image> The three-view drawings define a solid figure with diameter $D$ and height $H$. If the ratio of the solid's lateral surface area to the area of its circular base is 8:1, and the total volume of the solid is $13.5\\pi$ cubic units, what is the height (H) of the solid in units? You FIRST thi... | {
"ground_truth": "6",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "6",
"question": "<image> The three-view drawings define a solid figure with diameter $D$ and height $H$. If the ratio of the solid's lateral surface area to the area of its circular base is 8:1, and the total volume of the solid is $13.5\\pi$ cubic units, what is the height (H) of the solid in units?",... | |
2ce90439-7d75-4ec9-b873-e446ca388ef7 | MMFineReason_evol | math | [
{
"content": "<image> If $AC=3\\ \\unit{cm}$ and $BC=4\\ \\unit{cm}$, what is the exact positive difference, in $\\unit{cm}$, between the lengths of the segments $DB$ and $AD$ created on the hypotenuse $AB$ by the altitude $CD$? You FIRST think about the reasoning process as an internal monologue and then provi... | {
"ground_truth": "7/5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "7/5",
"question": "<image> If $AC=3\\ \\unit{cm}$ and $BC=4\\ \\unit{cm}$, what is the exact positive difference, in $\\unit{cm}$, between the lengths of the segments $DB$ and $AD$ created on the hypotenuse $AB$ by the altitude $CD$?",
"index": 65,
"split": "train",
"task": "{\"domain\": [\"Math\... | |
050bc997-755c-4dc9-aae2-3a9da1ea5058 | MMFineReason_evol | math | [
{
"content": "<image> Assume the truncated cone shown is a right circular frustum where the length of the generatrix $AC$ (slant height $L$) is five times the radius of the top base ($r$), and the radius of the bottom base ($R$) is three times the radius of the top base ($r$). The total surface area of the frus... | {
"ground_truth": "30",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "30",
"question": "<image> Assume the truncated cone shown is a right circular frustum where the length of the generatrix $AC$ (slant height $L$) is five times the radius of the top base ($r$), and the radius of the bottom base ($R$) is three times the radius of the top base ($r$). The total surface are... | |
f8375f13-2c7b-4099-9ee6-33331611c826 | MMFineReason_evol | math | [
{
"content": "<image> Considering Figure (a) (Clock) and Figure (d) (Ferris Wheel), calculate the ratio of the centripetal acceleration of a rider on the Ferris wheel ($a_F$) to the centripetal acceleration of the tip of the minute hand ($a_M$). Assume the Ferris wheel operates with a uniform rotational period ... | {
"ground_truth": "0.01",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "0.01",
"question": "<image> Considering Figure (a) (Clock) and Figure (d) (Ferris Wheel), calculate the ratio of the centripetal acceleration of a rider on the Ferris wheel ($a_F$) to the centripetal acceleration of the tip of the minute hand ($a_M$). Assume the Ferris wheel operates with a uniform rot... | |
8858cea9-6daf-4579-ad54-a76bf78f1678 | MMFineReason_evol | math | [
{
"content": "<image> Assume the variable A is initialized to 1. If only the sequence of operations $A \\leftarrow A \\times 2$ and $A \\leftarrow A + 6$ (corresponding to lines 2 and 3 of the program) is executed sequentially 5 complete times (5 cycles of multiplication followed immediately by addition), what ... | {
"ground_truth": "218",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "218",
"question": "<image> Assume the variable A is initialized to 1. If only the sequence of operations $A \\leftarrow A \\times 2$ and $A \\leftarrow A + 6$ (corresponding to lines 2 and 3 of the program) is executed sequentially 5 complete times (5 cycles of multiplication followed immediately by ad... | |
d85188e0-ccae-4efb-b491-4fc08c62997c | MMFineReason_evol | math | [
{
"content": "<image> If the conditions for $\\triangle BDA \\sim \\triangle AEC$ are met, and given that $AD=AE$, what is the exact numerical value of the ratio $\\frac{BD \\cdot EC}{AD^2}$? You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning pr... | {
"ground_truth": "1",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "1",
"question": "<image> If the conditions for $\\triangle BDA \\sim \\triangle AEC$ are met, and given that $AD=AE$, what is the exact numerical value of the ratio $\\frac{BD \\cdot EC}{AD^2}$?",
"index": 69,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
} | |
992a6fbd-4e58-43db-9c81-008ada99a0e4 | MMFineReason_evol | math | [
{
"content": "<image> If the line $y = ax$ and the hyperbola $y = \\frac{k}{x}$ ($x > 0$) intersect at point $A(1, 2)$ as shown, what is the exact numerical area of the triangle bounded by the x-axis, the y-axis, and the line that passes through point $A$ and is perpendicular to $y = ax$? You FIRST think about ... | {
"ground_truth": "25/4",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "25/4",
"question": "<image> If the line $y = ax$ and the hyperbola $y = \\frac{k}{x}$ ($x > 0$) intersect at point $A(1, 2)$ as shown, what is the exact numerical area of the triangle bounded by the x-axis, the y-axis, and the line that passes through point $A$ and is perpendicular to $y = ax$?",
"in... | |
07fbbc57-dcbf-4b35-8f2e-3b09e856d376 | MMFineReason_evol | math | [
{
"content": "<image> If the circle's radius $R$ is defined by the magnitude of the vector $\\overrightarrow{v}=(1, \\sqrt{3})$, and the inclination angle of the position vector $\\overrightarrow{OB}$ (defined by $\\overrightarrow{u}$) is exactly half the inclination angle of $\\overrightarrow{OA}$ (defined by ... | {
"ground_truth": "\\frac{\\pi}{3}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{\\pi}{3}",
"question": "<image> If the circle's radius $R$ is defined by the magnitude of the vector $\\overrightarrow{v}=(1, \\sqrt{3})$, and the inclination angle of the position vector $\\overrightarrow{OB}$ (defined by $\\overrightarrow{u}$) is exactly half the inclination angle of $\\overri... | |
a891eb37-e3f1-4c0c-b186-cb94ae015e01 | MMFineReason_evol | math | [
{
"content": "<image> Given the explicit dimension constraint $a=r$ shown in the figure, calculate the ratio of the excess volume of the sphere compared to the volume of the cube, expressed as a percentage of the sphere's total volume. (I.e., what percentage of $V_{\\text{sphere}}$ must be removed to equal $V_{... | {
"ground_truth": "76.1\\%",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "76.1\\%",
"question": "<image> Given the explicit dimension constraint $a=r$ shown in the figure, calculate the ratio of the excess volume of the sphere compared to the volume of the cube, expressed as a percentage of the sphere's total volume. (I.e., what percentage of $V_{\\text{sphere}}$ must be rem... | |
a407f822-292c-4835-bcd6-132f8b0837db | MMFineReason_evol | math | [
{
"content": "<image> Point P(12, 5) lies on the graph of the inverse proportion function shown. Let Q be a second point on the same curve such that its x-coordinate is 3. If the line segment PQ intersects the y-axis at point I, what is the exact length of the segment OI? You FIRST think about the reasoning pro... | {
"ground_truth": "25",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "25",
"question": "<image> Point P(12, 5) lies on the graph of the inverse proportion function shown. Let Q be a second point on the same curve such that its x-coordinate is 3. If the line segment PQ intersects the y-axis at point I, what is the exact length of the segment OI?",
"index": 73,
"split"... | |
bfd944de-357d-4f3f-a22b-7cf8a42487fb | MMFineReason_evol | math | [
{
"content": "<image> Calculate the area of a hypothetical rectangle whose width is equal to the height of the parallelogram (in cm) and whose length is equal to the numerical difference between the parallelogram's total area (in cm²) and its perimeter (in cm). You FIRST think about the reasoning process as an ... | {
"ground_truth": "3585",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "3585",
"question": "<image> Calculate the area of a hypothetical rectangle whose width is equal to the height of the parallelogram (in cm) and whose length is equal to the numerical difference between the parallelogram's total area (in cm²) and its perimeter (in cm).",
"index": 74,
"split": "train"... | |
ad4e18dd-8a18-45c9-b0cc-72c0cdf168d5 | MMFineReason_evol | math | [
{
"content": "<image> The three lines shown (green belt $l: x + 2y + 1 = 0$, the new perpendicular green belt $m$ passing through $P(2, 1)$, and the line $y=1$) enclose a triangular area used for specialized planting. Given the coordinates are in meters, what is the exact area, in square meters, of this enclose... | {
"ground_truth": "5",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "5",
"question": "<image> The three lines shown (green belt $l: x + 2y + 1 = 0$, the new perpendicular green belt $m$ passing through $P(2, 1)$, and the line $y=1$) enclose a triangular area used for specialized planting. Given the coordinates are in meters, what is the exact area, in square meters, of ... | |
874e3f07-4e8a-491b-9923-92413925e810 | MMFineReason_evol | math | [
{
"content": "<image> Given the central similarity shown with center $$O$$ and the ratio $$\\dfrac{OE}{OA}=\\dfrac{3}{5}$$ . If $P$ represents the perimeter and $A$ represents the area, suppose the difference in perimeters is $P_{ABCD} - P_{EFGH} = 12$ units, and the difference in areas is $A_{ABCD} - A_{EFGH} ... | {
"ground_truth": "300",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "300",
"question": "<image> Given the central similarity shown with center $$O$$ and the ratio $$\\dfrac{OE}{OA}=\\dfrac{3}{5}$$ . If $P$ represents the perimeter and $A$ represents the area, suppose the difference in perimeters is $P_{ABCD} - P_{EFGH} = 12$ units, and the difference in areas is $A_{ABC... | |
4c644aef-7887-4067-b9c6-c9a42acefba3 | MMFineReason_evol | math | [
{
"content": "<image> In the rectangle ABCD shown, if the area is $2\\sqrt{3}$ and the angle $\\angle BAC$ measures $30^\\circ$, what is the precise length of the segment AO? You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enc... | {
"ground_truth": "\\sqrt{2}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\sqrt{2}",
"question": "<image> In the rectangle ABCD shown, if the area is $2\\sqrt{3}$ and the angle $\\angle BAC$ measures $30^\\circ$, what is the precise length of the segment AO?",
"index": 77,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
} | |
e814d180-7846-4324-b2d1-7b7b749d838b | MMFineReason_evol | math | [
{
"content": "<image> Let $A_{Shared}$ be the measure of the angle formed at the intersection of the two main lines. Let $A_{Supp}$ be the angle supplementary to $A_{Shared}$. Find the sum of $m \\angle 1$ and $A_{Supp}$. You FIRST think about the reasoning process as an internal monologue and then provide the ... | {
"ground_truth": "202",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "202",
"question": "<image> Let $A_{Shared}$ be the measure of the angle formed at the intersection of the two main lines. Let $A_{Supp}$ be the angle supplementary to $A_{Shared}$. Find the sum of $m \\angle 1$ and $A_{Supp}$.",
"index": 78,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"t... | |
6c5ec868-93c5-40cf-b9cb-d97e10e04c7d | MMFineReason_evol | math | [
{
"content": "<image> Based on the geometric construction where M and N are midpoints of segments OA and OB respectively, and Xiao Ming measures $MN = 20m$, what is the exact numerical ratio of the area of the entire pond-side triangle $OAB$ to the area of the quadrilateral region $ABNM$? You FIRST think about ... | {
"ground_truth": "\\frac{4}{3}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{4}{3}",
"question": "<image> Based on the geometric construction where M and N are midpoints of segments OA and OB respectively, and Xiao Ming measures $MN = 20m$, what is the exact numerical ratio of the area of the entire pond-side triangle $OAB$ to the area of the quadrilateral region $ABNM$?... | |
fcee5694-62cf-4049-97a6-16c7d659fea6 | MMFineReason_evol | math | [
{
"content": "<image> Given the constraints in the figure that the overlapping area is equivalent to $\\frac{1}{12}$ of the larger parallelogram and $\\frac{1}{8}$ of the smaller parallelogram, calculate the ratio of the area of the union of the two parallelograms (the total area covered) to the area of the por... | {
"ground_truth": "19/11",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "19/11",
"question": "<image> Given the constraints in the figure that the overlapping area is equivalent to $\\frac{1}{12}$ of the larger parallelogram and $\\frac{1}{8}$ of the smaller parallelogram, calculate the ratio of the area of the union of the two parallelograms (the total area covered) to the... | |
1ab8efb4-c2f3-4886-be08-030ae9a02409 | MMFineReason_evol | math | [
{
"content": "<image> After calculating the height of the flagpole AB using the initial setup (CD=3m, OD=6m, DB=12m), Xiaoming determines the total distance OB. If the 3-meter pole CD were relocated to a new position $D'$ such that $D'$ is the midpoint of OB, the required height of the pole $C'D'$ needed to mai... | {
"ground_truth": "50%",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "50%",
"question": "<image> After calculating the height of the flagpole AB using the initial setup (CD=3m, OD=6m, DB=12m), Xiaoming determines the total distance OB. If the 3-meter pole CD were relocated to a new position $D'$ such that $D'$ is the midpoint of OB, the required height of the pole $C'D'$... | |
9cecd4d7-143c-4e1f-ac0b-f08cbb2b5496 | MMFineReason_evol | math | [
{
"content": "<image> Given that points $A$, $B$, and $C$ lie on the circle $O$, where $AB=4$ and the inscribed angle $\\angle ACB=45^{\\circ}$, calculate the exact area of the smaller circular segment bounded by the chord $AB$ and the minor arc $AB$. (Express the answer in the form $X\\pi - Y$, where $X$ and $... | {
"ground_truth": "2π - 4",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "2π - 4",
"question": "<image> Given that points $A$, $B$, and $C$ lie on the circle $O$, where $AB=4$ and the inscribed angle $\\angle ACB=45^{\\circ}$, calculate the exact area of the smaller circular segment bounded by the chord $AB$ and the minor arc $AB$. (Express the answer in the form $X\\pi - Y$... | |
e90a069e-df59-4473-914a-adb01b7cc097 | MMFineReason_evol | math | [
{
"content": "<image> Determine the area of the parallelogram in square inches. Round your final answer to the nearest hundredth. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final... | {
"ground_truth": "106.07",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "106.07",
"question": "<image> Determine the area of the parallelogram in square inches. Round your final answer to the nearest hundredth.",
"index": 83,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
} | |
ae8471d1-0c2e-4ea3-a084-16626a96e78a | MMFineReason_evol | math | [
{
"content": "<image> Given $\\triangle ABC$ with $AC=6$cm, $AB=8$cm, and $BC=10$cm, and $DE$ is the perpendicular bisector of side $AB$. If $E$ is the intersection of $AB$ and $DE$, and $D$ is the intersection of $BC$ and $DE$, calculate the area of $\\vartriangle ADE$ in square centimeters. You FIRST think ab... | {
"ground_truth": "6 cm²",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "6 cm²",
"question": "<image> Given $\\triangle ABC$ with $AC=6$cm, $AB=8$cm, and $BC=10$cm, and $DE$ is the perpendicular bisector of side $AB$. If $E$ is the intersection of $AB$ and $DE$, and $D$ is the intersection of $BC$ and $DE$, calculate the area of $\\vartriangle ADE$ in square centimeters.",
... | |
6e180a1d-9846-4cbf-acb6-93f20d90e236 | MMFineReason_evol | math | [
{
"content": "<image> A hexagonal prism is shown in the figure below. The side lengths of its base are all 3 cm, and the side edges are 5 cm long. If the volume of this prism is calculated and expressed in the simplest exact radical form $\\frac{A\\sqrt{B}}{C}$ cm³, where A, B, and C are integers, what is the v... | {
"ground_truth": "135",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "135",
"question": "<image> A hexagonal prism is shown in the figure below. The side lengths of its base are all 3 cm, and the side edges are 5 cm long. If the volume of this prism is calculated and expressed in the simplest exact radical form $\\frac{A\\sqrt{B}}{C}$ cm³, where A, B, and C are integers,... | |
691cb663-9932-444d-8d3b-f62e302692fd | MMFineReason_evol | math | [
{
"content": "<image> Determine the exact, simplified value of the expression \\(\\frac{y}{x} + \\frac{x}{y}\\). You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. The final answer MUST BE p... | {
"ground_truth": "5/2 (equivalent to 2.5)",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "5/2 (equivalent to 2.5)",
"question": "<image> Determine the exact, simplified value of the expression \\(\\frac{y}{x} + \\frac{x}{y}\\).",
"index": 86,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"type\": \"instruction\"}"
} | |
d8b250bd-daae-431c-a3f1-234f683ae55e | MMFineReason_evol | math | [
{
"content": "<image> If the operation $+(-2\\frac{1}{2})$ were hypothetically replaced by an operation that multiplies the current value by the reciprocal of the absolute value of the number originally shown in that box, what starting input value of $$x$$ would be necessary to achieve a final output value of $... | {
"ground_truth": "25",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "25",
"question": "<image> If the operation $+(-2\\frac{1}{2})$ were hypothetically replaced by an operation that multiplies the current value by the reciprocal of the absolute value of the number originally shown in that box, what starting input value of $$x$$ would be necessary to achieve a final outp... | |
bc2a306b-c324-4a50-9216-c6ee2840c460 | MMFineReason_evol | math | [
{
"content": "<image> The folding fan's functional paper material covers the region bounded by the full radius OB and the arc of the dark reinforced base near O. Assuming the radius of this inner base ($r$) is visually proportionate to exactly one-sixth of the total radius ($OB = R = 30\\text{ cm}$), and the fa... | {
"ground_truth": "\\frac{875}{3}\\pi",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{875}{3}\\pi",
"question": "<image> The folding fan's functional paper material covers the region bounded by the full radius OB and the arc of the dark reinforced base near O. Assuming the radius of this inner base ($r$) is visually proportionate to exactly one-sixth of the total radius ($OB = R ... | |
3cafd8cf-d2ed-4d7c-8215-29f70b82ead6 | MMFineReason_evol | math | [
{
"content": "<image> Elsa has 3 tetrahedra and 5 dice. If V is the total number of vertices, E is the total number of edges, and F is the total number of faces present across all eight objects, what is the value of $(V + F) - E$? You FIRST think about the reasoning process as an internal monologue and then pro... | {
"ground_truth": "16",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "16",
"question": "<image> Elsa has 3 tetrahedra and 5 dice. If V is the total number of vertices, E is the total number of edges, and F is the total number of faces present across all eight objects, what is the value of $(V + F) - E$?",
"index": 89,
"split": "train",
"task": "{\"domain\": [\"Math... | |
91003a54-4644-4b4f-8f64-7938064c8815 | MMFineReason_evol | math | [
{
"content": "<image> Given the right triangle DEF where $\\angle D = 90^{\\circ}$, $\\angle E = 30^{\\circ}$, and the length of the hypotenuse $EF$ is 10. Determine the exact length of the radius of the circle inscribed within $\\triangle DEF$. You FIRST think about the reasoning process as an internal monolog... | {
"ground_truth": "\\frac{5(\\sqrt{3} - 1)}{2}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{5(\\sqrt{3} - 1)}{2}",
"question": "<image> Given the right triangle DEF where $\\angle D = 90^{\\circ}$, $\\angle E = 30^{\\circ}$, and the length of the hypotenuse $EF$ is 10. Determine the exact length of the radius of the circle inscribed within $\\triangle DEF$.",
"index": 90,
"split": ... | |
fcd61824-2fcb-4f07-b015-d24314b193d7 | MMFineReason_evol | math | [
{
"content": "<image> If the total area of the wall hanging shown is $2816 \\text{ cm}^2$, the area of the frame border (the region of width $x$ surrounding the $60 \\text{ cm} \\times 40 \\text{ cm}$ embroidery) is what simplified fraction of the area of the embroidery itself? You FIRST think about the reasoni... | {
"ground_truth": "\\frac{13}{75}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{13}{75}",
"question": "<image> If the total area of the wall hanging shown is $2816 \\text{ cm}^2$, the area of the frame border (the region of width $x$ surrounding the $60 \\text{ cm} \\times 40 \\text{ cm}$ embroidery) is what simplified fraction of the area of the embroidery itself?",
"ind... | |
fa838d4c-e6e3-4d34-8632-adc14375d2f1 | MMFineReason_evol | math | [
{
"content": "<image> To measure the distance between points A and B on the lakeside, the surveyor establishes point O such that A, O, C and B, O, D are respectively collinear. If it is mathematically confirmed that the area of $\\triangle AOB$ is 9 times the area of $\\triangle COD$, and the difference between... | {
"ground_truth": "450 meters",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "450 meters",
"question": "<image> To measure the distance between points A and B on the lakeside, the surveyor establishes point O such that A, O, C and B, O, D are respectively collinear. If it is mathematically confirmed that the area of $\\triangle AOB$ is 9 times the area of $\\triangle COD$, and t... | |
795d2037-f9b1-48e0-bf91-23f9817934f8 | MMFineReason_evol | math | [
{
"content": "<image> As shown in the figure, $A, B, C, D$ are four points on the circle $⊙O$, and $\\angle C=110^{\\circ}$. If $K$ represents the total area of circle $⊙O$, what is the exact area of the circular sector $OBD$ corresponding to the minor arc $BD$, expressed as a fraction $\\frac{P}{Q}$ of $K$? (T... | {
"ground_truth": "7/18",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "7/18",
"question": "<image> As shown in the figure, $A, B, C, D$ are four points on the circle $⊙O$, and $\\angle C=110^{\\circ}$. If $K$ represents the total area of circle $⊙O$, what is the exact area of the circular sector $OBD$ corresponding to the minor arc $BD$, expressed as a fraction $\\frac{P}... | |
614a24d3-1159-4411-b609-793ff173df17 | MMFineReason_evol | math | [
{
"content": "<image> Given that the total sample size surveyed was 5000 students, calculate the absolute difference in the number of students between the category displaying the largest percentage share ('了解') and the category labeled '不太了解' (Limited Understanding). You FIRST think about the reasoning process ... | {
"ground_truth": "2250",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "2250",
"question": "<image> Given that the total sample size surveyed was 5000 students, calculate the absolute difference in the number of students between the category displaying the largest percentage share ('了解') and the category labeled '不太了解' (Limited Understanding).",
"index": 94,
"split": "... | |
26972329-eb76-44d1-adc9-213922ee507d | MMFineReason_evol | math | [
{
"content": "<image> Given the price ($x$) and sales volume ($y$) data, calculate the value of the y-intercept ($a$) for the optimal linear regression line $\\hat{y} = \\hat{b}x + a$ derived using the least-squares method. You FIRST think about the reasoning process as an internal monologue and then provide th... | {
"ground_truth": "40",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "40",
"question": "<image> Given the price ($x$) and sales volume ($y$) data, calculate the value of the y-intercept ($a$) for the optimal linear regression line $\\hat{y} = \\hat{b}x + a$ derived using the least-squares method.",
"index": 95,
"split": "train",
"task": "{\"domain\": [\"Math\"], \"... | |
85c724cb-9b7a-4bc8-b3e0-4cfe4731595e | MMFineReason_evol | math | [
{
"content": "<image> Assuming the visual representation implies that the diagonals mutually bisect each other, and given that BD = 8, AC = 6, and ∠BOC = 120°, calculate the exact length of the longer side of quadrilateral ABCD. (Leave the answer in simplified radical form.) You FIRST think about the reasoning ... | {
"ground_truth": "\\sqrt{37}",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\sqrt{37}",
"question": "<image> Assuming the visual representation implies that the diagonals mutually bisect each other, and given that BD = 8, AC = 6, and ∠BOC = 120°, calculate the exact length of the longer side of quadrilateral ABCD. (Leave the answer in simplified radical form.)",
"index": 96... | |
8b382215-0921-46a9-87f0-cbb860ea39bc | MMFineReason_evol | math | [
{
"content": "<image> Given the cylinder shown ($r=1$), assume a height $h$ such that the cylinder's total surface area ($SA$) is exactly three times its volume ($V$). If this calculated height were subsequently doubled, what would be the resulting numerical value of the lateral surface area ($LSA$)? You FIRST ... | {
"ground_truth": "8π",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "8π",
"question": "<image> Given the cylinder shown ($r=1$), assume a height $h$ such that the cylinder's total surface area ($SA$) is exactly three times its volume ($V$). If this calculated height were subsequently doubled, what would be the resulting numerical value of the lateral surface area ($LSA$... | |
c2e33414-b850-43dc-9f04-68a28f429be1 | MMFineReason_evol | math | [
{
"content": "<image> Assume that quadrilateral $ABCD$ is a rectangle (as shown) such that the ratio of the side lengths $AD : AB$ is $\\sqrt{3}:1$. If the diagonals $AC$ and $BD$ intersect at point $O$, what is the measure of the angle $\\angle AOB$ in degrees? You FIRST think about the reasoning process as an... | {
"ground_truth": "60",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "60",
"question": "<image> Assume that quadrilateral $ABCD$ is a rectangle (as shown) such that the ratio of the side lengths $AD : AB$ is $\\sqrt{3}:1$. If the diagonals $AC$ and $BD$ intersect at point $O$, what is the measure of the angle $\\angle AOB$ in degrees?",
"index": 98,
"split": "train",... | |
56ba80be-1a1d-45ed-a857-7aee8ee68f1c | MMFineReason_evol | math | [
{
"content": "<image> If the frustum shown (defined by $r_1=2, r_2=4, h=4$) was derived from a complete cone by cutting parallel to the base, calculate the exact volume of the original, complete cone from which the frustum was sectioned. Express the answer as a fraction multiplied by $\\pi$ (e.g., $K\\pi$, wher... | {
"ground_truth": "\\frac{128}{3}\\pi",
"style": "rule"
} | {
"dataset": "OpenDataArena/MMFineReason",
"subset": "Euclid30K",
"split": "train",
"license": "unknown"
} | {
"answer": "\\frac{128}{3}\\pi",
"question": "<image> If the frustum shown (defined by $r_1=2, r_2=4, h=4$) was derived from a complete cone by cutting parallel to the base, calculate the exact volume of the original, complete cone from which the frustum was sectioned. Express the answer as a fraction multiplied b... |
End of preview. Expand in Data Studio
VeriEvol-RL
RL training data for VeriEvol: Scaling Multimodal Mathematical Reasoning via Verifiable Evol-Instruct. This is the reinforcement-learning stage dataset used for GRPO-style training on top of the SFT-initialized policy (see the companion SFT set Ringo1110/VeriEvol-SFT).
📄 Paper: arXiv:2606.23543 💻 Code: github.com/lihaoling/VeriEvol
Each example is a single-image visual math/reasoning problem with a verifiable ground-truth answer, formatted for the verl RL framework. Prompts are produced by VeriEvol's type-aware evolution operators and every answer has passed the HTV-Agent hypothesis-test verifier, so the reward labels are reliable at scale.
About the paper
Scaling RL for visual mathematical reasoning requires more than harder questions — as data volume grows, the reward labels themselves must stay reliable. VeriEvol treats scaling as a verifiable data-construction problem and decouples two axes before any policy update: prompt difficulty (expanded by route-specific evolution operators) and answer reliability (enforced offline by HTV-Agent, which accepts an answer only after multi-source counter-evidence fails to refute it). The verified data plugs directly into standard GRPO-style RL recipes.
Key results (five-benchmark visual-math suite): with backbone, SFT initialization, and GRPO recipe held fixed, VeriEvol adds a cumulative +3.88 over an un-evolved RL baseline — +1.82 from evolved prompts and +2.06 from the HTV-Agent verifier.
Dataset summary
- Examples: 133,862
- Modality: image + text (exactly one image per example)
- Images: embedded inline as native image bytes via the HuggingFace
datasetsImage()feature — the file is fully self-contained (no separate image download needed) and images render directly in the dataset viewer. - Format: verl-style RL parquet
(
prompt/reward_model/data_source/extra_info/images) - Ability mix:
math(109,369),reasoning(15,967),mathematics(8,526) - Source subsets (evolved from public visual-math corpora via MMFineReason): WaltonColdStart (42,408), ViRL39K (29,603), Euclid30K (18,220), thinklite_vl_hard (8,496), FineVision-geo170k(qa) (7,928), FineVision-geometry3k(mathv360k) (5,952), mmopenr1-8k (5,258), tqa_train (5,156), mmk12 (2,315), …
- Ground truth: every row has a non-empty
reward_model.ground_truth(rule-based verifiable answer).
Data structure
| field | type | description |
|---|---|---|
images |
list[Image] |
native image bytes (HF Image() feature), one per example |
prompt |
list[{role, content}] |
chat-format user turn: <image> + question + <think>…</think> / \boxed{} instructions |
reward_model |
{ground_truth, style} |
ground_truth = the verifiable answer; style = rule |
data_source |
str |
MMFineReason_evol (routes reward computation in verl) |
ability |
str |
math / reasoning / mathematics |
source |
{dataset, subset, split, license} |
provenance of the seed problem (public dataset id + subset) |
extra_info |
{answer, question, index, split, task} |
auxiliary fields |
id |
str |
unique example id |
Usage
from datasets import load_dataset
ds = load_dataset("Ringo1110/VeriEvol-RL", split="train")
ex = ds[0]
print(ex["prompt"][0]["content"]) # question with <image> placeholder
print(ex["reward_model"]["ground_truth"]) # verifiable answer
img = ex["images"][0] # PIL.Image, decoded automatically
img.show()
Using with verl
The parquet already follows the verl RL schema. Point your GRPO config's
data.train_files at this parquet; data_source = MMFineReason_evol selects the
matching reward function, and reward_model.ground_truth supplies the rule-based
reward signal.
Source & licensing
- Seed problems are evolved from public visual-math datasets (via the MMFineReason collection); please also observe those datasets' terms.
- Evolved prompts and verified answers are produced by the VeriEvol pipeline.
Citation
@article{li2026verievol,
title = {VeriEvol: Scaling Multimodal Mathematical Reasoning via Verifiable Evol-Instruct},
author = {Li, Haoling and Zheng, Kai and Wu, Jie and Xu, Can and Sun, Qingfeng and Hu, Han and Yang, Yujiu},
journal = {arXiv preprint arXiv:2606.23543},
year = {2026}
}
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