Explaining a Mathematical/Scientific Concept: Start with a precise prompt: "Explain [concept, e.g., 'Lagrangian mechanics'] to a [target audience, e.g., 'first-year engineering student'] using [analogy/example, e.g., 'a simple pendulum system'] and provide a [specific detail, e.g., 'derivation of its equation of motion']."
Solving a Step-by-Step Problem: Input the problem clearly: "Solve the following [type of problem, e.g., 'definite integral'] step-by-step, showing all intermediate calculations: [problem statement]. Explain each major step's reasoning."
Generating Code Snippets: Define the programming language and desired functionality: "Write a [language, e.g., 'Python'] function that [functionality, e.g., 'calculates the nth Fibonacci number recursively']. Include docstrings and type hints."
Debugging Code: Provide the problematic code and the error message: "I'm getting a '[error type, e.g., 'TypeError: 'str' object is not callable']' in this [language, e.g., 'JavaScript'] code: [paste code]. What is causing this and how can I fix it?"
Designing an Algorithm: Describe the problem and desired output: "Design an algorithm in pseudocode to [problem, e.g., 'find the shortest path between two nodes in a weighted graph']. Explain its time complexity and space complexity."
Understanding Code: Paste the code and ask for clarification: "Explain what this [language, e.g., 'C++'] code does, line by line, and describe its overall purpose: [paste code]."
Refining and Iterating: After receiving a response, ask follow-up questions for deeper understanding: "Can you provide an alternative approach?" or "What are the edge cases for this solution?" or "How would this change if [new condition]?"