Suppose I have a a probability distribution that I know to have a continuous differentiable unimodal pdf, with pdf(x) strictly greater than zero for all x in the positive half-plane. In addition, I have a black box that provides me with the CDF, pdf and quantile value for any given x.
However, I do not want those things. Instead I want the functions which are to the conditional means (or conditional totals) as the CDF and the survival function are to the conditional probability, i.e. the two functions that that provide the the mean (or total) values conditional on x being less than or greater than, respectively, some constant c. In other word, I am looking two functions of c, given the distribution.
Is there an efficient method, ideally analytic but probably numeric, to estimate these conditional mean values from what I can extract from my black box? You may assume the distribution has a finite mean, though it may be heavy-tailed.
If we are looking at a numeric approach, please assume that I can program, in R or a little in C++, but that I don't have any real training in numerical methods.
Also, I would like to know if these two conditional mean functions described above have commonly-used names in statistics, economics, or elsewhere. I need to do a bunch of things with them, and I am looking for a term or terms I can use to locate a literature.