An overview is presented of recent advances in Maple for both symbolic and numeric computation. A user-friendly syntax for matrix computations supplements state-of-the-art algorithms for linear algebra, for symbolic computation as well as for numerical linear algebra at hardware floating point speed. Capabilities for symbolic integration are supplemented by fast numerical integration exploiting the NAG numerical subroutine library. Techniques for computing exact symbolic solutions of differential equations include decision procedures for special types of DEs, the classification of DEs into known classes, and symmetry-based methods. New numerical solvers which have been incorporated into Maple 7 take full advantage of hardware floating point speed, for both IVPs and BVPs.