  The paper is concerned with thermostatistics of both $D$-dimensional Bose and
Fermi ideal gases in a confining potential of type $Ar^{n}+Br^{-n}$. The
investigation is performed in the framework of the semiclassical approximation.
Some physical quantities for such systems are derived, like density of states,
density profiles and number of particles. Bose-Einstein condensation (BEC) is
discussed in the high and low temperature regimes.
