Scaffold a graded problem set with sections, problems, worked solutions, and short "why this matters" explainers across analytical, empirical, and coding types. Use when user says "make a problem set on X", "scaffold exercises for this lecture", "create practice problems", "generate homework with a solution key", "build a graded assignment on topic Y". Emits a clean student set plus a separate solution key — NOT for grading submissions or auto-checking student answers.