Drive the error under tolerance by choosing a numerical integration method and subdivision count, all on a limited compute budget.
Each round sets an integral, a target error tolerance, and a compute budget. Pick a method, set the number of subdivisions, and run an estimate. Each run spends budget based on its cost; drive the absolute error below tolerance before the budget runs out. Smarter methods reach the target on far less budget than brute-force rectangles.
Quadrature is about numerical integration, teaching why the choice of method matters.
Choosing a method and a number of subdivisions to hit an error tolerance on a compute budget is numerical integration with its real constraint attached.
Charging for each run is the original economy.
The budget forces the actual engineering question. Methods differ in how fast their error shrinks as subdivisions increase — Simpson's rule converges much faster than the trapezoid rule on smooth functions — so the cheapest route to a tolerance is a choice of method, not just more effort.
Quadrature is an original free browser calculus game about numerical integration, teaching why method choice matters as much as raw effort when approximating the area under a curve.