We give a simple construction of an algebraic non- commutative deformation of the moduli space of flat connections on a Riemann surface over a ring of rational functions in a parameter q. We show that there is a natural trace functional on this algebra which has values in such holomorphic functions defined for 0 < |q| < 1, which have an asymptotic expansion as q approaches 1 along the real line. We give an interpretation of these results in the framework of formal products on symplectic manifolds.