  Under certain assumptions we derive a complete semiclassical asymptotics of
the spectral function $e_{h,\varepsilon}(x,x,\lambda)$ for a scalar operator
  \begin{equation*} A_\varepsilon (x,hD)= A^0(hD) + \varepsilon B(x,hD),
\end{equation*} where $A^0$ is an elliptic operator and $B(x,hD)$ is a periodic
or almost periodic perturbation.
  In particular, a complete semiclassical asymptotics of the integrated density
of states also holds. Further, we consider generalizations.
