It is shown how recent results on combinations of sequences of quadrature formulae with high polynomial exactnessrepresent an efficient technique for the fast computation of the so-called dilation integrals. These integrals wereintroduced in the modern robustness literature as a tool for addressing approximate robustness in problems involving polynomial parameter dependence. As a result, the calculations are simplified and more precise conclusions can be made about approximate robustness. Illustrative examples of the proposed approach are presented.