  The multiplicative structure of the trivial symplectic groupoid over $\mathbb
R^d$ associated to the zero Poisson structure can be expressed in terms of a
generating function. We address the problem of deforming such a generating
function in the direction of a non-trivial Poisson structure so that the
multiplication remains associative. We prove that such a deformation is unique
under some reasonable conditions and we give the explicit formula for it. This
formula turns out to be the semi-classical approximation of Kontsevich's
deformation formula. For the case of a linear Poisson structure, the deformed
generating function reduces exactly to the CBH formula of the associated Lie
algebra. The methods used to prove existence are interesting in their own right
as they come from an at first sight unrelated domain of mathematics: the
Runge--Kutta theory of the numeric integration of ODE's.
