The Wolfram Language deeply integrates regions into high-level solvers, including the ability to integrate or solve partial differential equations over regions, solve equations and inequalities with region constraints, or optimize over regions. The results can be either symbolic and exact or numeric and approximate.
NDSolve — solve a partial differential equation over a region
NDEigensystem — compute eigenvalues and eigenfunctions over a region
Solve — solve equations, inequalities, and region constraints
Minimize — minimize a function over a region
Plot3D — plot a function over a region
RegionNearest — find the nearest point in a region