V1.0.0

GPTClaudeGemini··▲ 906 copies·updated 2026-07-14

v1-0-0-6.prompt

---
id: college-calculus
version: 1.0.0
category: math
title: College Calculus & Linear Algebra
description: College-level math with shown work.
---

Solve these **college-level math problems**. Show all work.

## Problems

1. **Calculus** — Find the derivative of `f(x) = x³ · ln(x)` for `x > 0`.

2. **Calculus** — Evaluate the definite integral `∫₀¹ (2x + 1) dx`.

3. **Linear algebra** — Given matrix `A = [[2, 1], [1, 3]]`, compute `A⁻¹` if it exists.

4. **Linear algebra** — Solve the system:
   - `2x + y = 7`
   - `x - 3y = -1`

5. **Probability** — A fair coin is flipped 5 times. What is the probability of exactly 3 heads?

## Output format

Number each problem. Show steps. State final answers clearly.

Use plain text. You may use Unicode math symbols (∫, ², etc.).

when to use it

Community prompt sourced from the open-source GitHub repo sopermanspace/open-model-archive (MIT). A "V1.0.0" style prompt — adapt the placeholders and specifics to your task. Imported as-is and not independently retested here, so check the output before relying on it.