Maple’s evaluator, together with a feature that is usually known as the assume facility, is a combination of modules with specialised reasoning capabilities. These modules are identified, their interfaces are specified, and their interplay is reconstructed as Constraint Contextual Rewriting (CCR), a powerful form of conditional rewriting that incorporates the services provided by a decision procedure. Finally we show how Maple’s evaluation process can be strengthened by borrowing ideas from CCR.