Double integration through interpolation? Is it possibile with Matlab?

Consider the following z(x;y) function: z= f(x)*g(y), where f(x) is a Poisson distribution function, whilst g(y) is a a Log-Normal distribution function. I need to evaluate the double integral of f(x)*g(y) over the following non rectangular area: -0.5 < x < +inf 0 < y < M/x, where M is a real positive number.

As we all know the solution cannot be reached through integration.

The problem must be solved by using a suitable software, but I don't know whether or not Matlab is the right tool to use.

Obviously, we could calculate the coordinate of lots of points of both the f and g curves; so, if Matlab could interpolate a "smooth curve" and then evaluate the f(x) and g(y) for every x and y, the problem could be solved in a truly straightforward manner. Misfortunately, I know nothing about Matlab, as I have never used it and I have never read a manual about it.

I would like to receive a reliable answer from a Matlab-Expert!

Thank you in advance for your kind support.