We report calculations on the total (elastic plus inelastic) positron-scattering cross sections from several diatomic and polyatomic molecules (H&, H20, NH3, CH4, N2, CO, C2H2, O2, SiH4, CO&, N20, and CF4) where experimental data are available. The impact energy (E) range is 10 -5000 eV. A local spherical complex optical potential (SCOP) is calculated for each positron-molecule system from the target charge density [p(r)], which in turn is determined from the corresponding molecular wave function at the Hartree-Fock level. The real part of the SCOP is composed of the repulsive static and attractive positron-correlation-polarization potential of Jain [Phys. Rev. A 39, 2437 (1990)]. The imaginary component of the SCOP, the so-called absorption potential, is derived semiempirically as a function of p(r), E, and the mean excitation energy. The resulting complex optical potential is treated exactly in a variable-phase approach to yield complex phase shift and the total-cross-section quantities. In this intermediateand high-energy region, the small contribution due to the nonspherical nature of the target is neglected. In addition, we fit the total-cross-section values to a simple analytic formula. For molecules possessing a permanent dipole or quadrupole moment, the present results are reliable only roughly above 50 eV. PACS number(s): 34.80.i, 34.90.+ q, 61.80.Fe