  We express integrals of definable functions over definable sets uniformly for
non-Archimedean local fields, extending results of Pas. We apply this to
Chevalley groups, in particular proving that zeta functions counting conjugacy
classes in congruence quotients of such groups depend only on the size of the
residue field, for sufficiently large residue characteristic. In particular,
the number of conjugacy classes in a congruence quotient depends only on the
size of the residue field. The same holds for zeta functions counting
dimensions of Hecke modules of intertwining operators associated to induced
representations of such quotients.
