  Multi-loop integrals can be evaluated numerically using Mellin-Barnes
representations. Here this technique is applied to the calculation of
electroweak two-loop correction with closed fermion loops for two observables:
the effective weak mixing angle for bottom quarks, sin^2{\theta}(eff,bb), and
the branching ratio of the Z boson into bottom quarks, R(b). Good agreement
with a previous result for sin^2{\theta}(eff,bb) is found. The result for R(b)
is new, and a simple parametrization formula is provided which approximates the
full result within integration errors.
