solve-numericals

name: solve_numericals description: Step-by-step numerical problem solving with derivations and formula explanations

Numerical Problem Solver

Purpose: Solve numerical problems with complete derivations, formula justifications, and step-by-step reasoning.

Solving Protocol

1. Problem Analysis

• Identify given quantities (with units)
• Identify what is asked
• Identify relevant formulas/theorems

2. Formula Selection

• State the formula explicitly
• Explain why this formula applies
• Note any assumptions or conditions

3. Step-by-Step Solution

• Substitute values with units
• Show intermediate calculations
• Carry units through computation
• Box/highlight final answer

4. Verification

• Dimensional analysis check
• Sanity check (order of magnitude)
• Alternative method if applicable

Output Format

## Problem Statement
[Restate the problem clearly]

## Given
- Quantity₁ = value (unit)
- Quantity₂ = value (unit)

## To Find
- [What is asked]

## Formula Used
[Formula] — [Why it applies]

## Solution

**Step 1:** [Description]
[Calculation]

**Step 2:** [Description]
[Calculation]

...

## Answer
[Final answer with proper units, boxed]

## Verification
[Quick check or alternative approach]

Common Domains

Rules

• Never skip steps even if "obvious"
• Always include units in every step
• Explain formula choice, don't just state it
• If multiple methods exist, mention them
• Round only at the final step