Scanning solution set of inequality system by a combined code

Numerical methods often reduce the solving of a complicated problem to a set of elementary problems. In previous papers, the author reduced some problems of numerical analysis (e.g. the computation of integral value with error bound) to computing solution boxes of one inequality. The paper contains a new algorithm for application of solution boxes of one inequality. This algorithm can be useful in itself and can be used as the base of other investigations. Nevertheless, the real worth of the paper is that the first completely automatic, effective code in the topic is given here by connecting a Maple 13 code and a Visual C++ 2008 code.