  We show the power of Bruno Buchberger's seminal Groebner Basis algorithm,
interfaced, seamlessly, with what we call symbolic dynamical programming, to
automatically generate algebraic equations satisfied by the generating
functions enumerating so-called Generalized Dyck Walks, i.e. 2D walks that
start and end on the x-axis, and never dip below it, for an arbitrary set of
steps. More impressively, we combine it with calculus (that Maple knows very
well!), to automatically compute generating functions for the sum-of-the-areas
of these generalized Dyck paths, and even for the sum of any given power of the
areas, enabling us to get statistical information about the area under a random
generalized Dyck path.
