Abstract: A system for computing multiple integrals employs an algorithm which selects a plurality of predetermined parameters, corresponding to selectable levels of accuracy of an approximation at the solution. The parameter values are selected and stored, along with a smoothing index, which may be zero. An arithmetic logic unit, which can perform a variety of functions under control of an instruction decoder, forms a plurality of functions in the form of unique polynomials, under predetermined conditions, such that a value (SI) can be determined for the multiple integral. The parameters are selected in response to a judgment on the part of the user of a required minimum level of accuracy in the context of the increases in computing time which would be required to achieve higher levels of accuracy.