Joint with Felix Wierstra, we propose a framework for a complete set of integrals which distinguish rational homotopy classes of maps between simply connected manifolds. This set of integrals generalizes Whitehead’s formula for the Hopf invariant, as first generalized to all homotopy groups by Ben Walter and myself. The set-up is very general, with basic definitions applying to maps for differential graded algebras over an operad. Conjecturally, our integrals calculate the Maurer-Cartan solution (up to guage equivalence) which corresponds to such a map.