Magnetization noncollinearity in ferromagnet-superconductor (F/S) heterostructures is expected to enhance the superconducting transition temperature (T(c)) according to the domain-wall superconductivity theory, or to suppress T(c) when spin-triplet Cooper pairs are explicitly considered. We study the proximity effect in F/S structures where the F layer is a Sm-Co/Py exchange-spring bilayer and the S layer is Nb. The exchange-spring contains a single, controllable and quantifiable domain wall in the Py layer. We observe an enhancement of superconductivity that is nonmonotonic as the Py domain wall is increasingly twisted via rotating a magnetic field, different from theoretical predictions. We have excluded magnetic fields and vortex motion as the source of the nonmonotonic behavior. This unanticipated proximity behavior suggests that new physics is yet to be captured in the theoretical treatments of F/S systems containing noncollinear magnetization.