  We extend a method for modeling synchrotron and synchrotron self-Compton
radiations in blazar jets to include external Compton processes. The basic
model assumption is that the blazar radio through soft X-ray flux is nonthermal
synchrotron radiation emitted by isotropically-distributed electrons in the
randomly directed magnetic field of outflowing relativistic blazar jet plasma.
Thus the electron distribution is given by the synchrotron spectrum, depending
only on the Doppler factor $\delta_{\rm D}$ and mean magnetic field $B$, given
that the comoving emission region size scale $R_b^\prime \lesssim c \dD
t_v/(1+z)$, where $t_v$ is variability time and $z$ is source redshift.
Generalizing the approach of Georganopoulos, Kirk, and Mastichiadis (2001) to
arbitrary anisotropic target radiation fields, we use the electron spectrum
implied by the synchrotron component to derive accurate Compton-scattered
$\gamma$-ray spectra throughout the Thomson and Klein-Nishina regimes for
external Compton scattering processes. We derive and calculate accurate
$\gamma$-ray spectra produced by relativistic electrons that Compton-scatter
(i) a point source of radiation located radially behind the jet, (ii) photons
from a thermal Shakura-Sunyaev accretion disk and (iii) target photons from the
central source scattered by a spherically-symmetric shell of broad line region
(BLR) gas. Calculations of broadband spectral energy distributions from the
radio through $\gamma$-ray regimes are presented, which include self-consistent
$\gamma\gamma$ absorption on the same radiation fields that provide target
photons for Compton scattering. Application of this baseline flat spectrum
radio/$\gamma$-ray quasar model is considered in view of data from $\gamma$-ray
telescopes and contemporaneous multi-wavelength campaigns.
