A non-abelian and supersymmetric Stokes theorem for physics and mathematics?

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Everyone in mathematics (differential geometry) and theoretical physics is aware of the generalized Stokes theorem for differential forms, namely $$\int_\Sigma d\omega=\int_{\partial \Sigma}\omega$$ Question, is there any generalization of it for the following cases?

a) Superforms.

b) Non-abelian differential operators, $D_A=dA+A^2$.