This talk is set at a basic level. Differentiation and Integration are
often the earliest and possibly the best understood topics in elementary calculus. So it may come as a surprise to some that serious problems may be encountered in programming Numerical Quadrature and Numerical Differentiation.

Among the topics treated are the performance profile of the automatic
quadrature routine; a software interface problem; round-off error amplification in numerical differentiation; and, at the very end, possibilities for using complex variable analysis.

These lead to generally conceptual problems. The questions which arise can be understood with minimal mathematical sophistication. But a particular answer, if one exists, might be complicated. In this talk we concentrate on the questions.