  In this paper, we demonstrated that the multiple turning point problems
within the framework of the Wentzel-Kramers-Brillouin (WKB) approximation
method can be reduced to two turning point one for a non-symmetric potential
function by using an appropriate Pekeris-type approximation scheme. We solved
the Schr\"odinger equation with the Killingbeck potential plus an inversely
quadratic potential (KPIQP) function. The special cases of the modeled
potential are discussed. We obtained the energy eigenvalues and the mass
spectra of the heavy and heavy-light mesons systems. The results in this
present work are in good agreement with the results obtained by other
analytical methods and available experimental data in the literature
