Using an integral formulation of random testing for regular continuous input, we present an approximate solution that enables highly accurate estimations of the results for arbitrary operational profiles, using strategically chosen input in a single test suite. The current approach, building on the Lagrange interpolation and Gaussian integration theorems, thus solves the long-standing issue of the necessity of unique test suites for fundamentally different operational profiles in random testing. Empirical comparisons are furthermore performed for a total of 27 profiles on five seeded faults in a numerical routine and a straightforward modulus fault. Using a high enough expansion in the approximation, the resulting failure frequencies and variances became statistically identical with the "ordinary" evaluations in all cases. It thus becomes possible to eliminate any extra test cases and still keep full accuracy when changing between operational profiles.