  Inspired by the Maxwell symmetry generalization of general relativity
(Maxwell gravity), we have constructed the Maxwell extension of $f(R)$ gravity.
We found that the semi-simple extension of the Poincare symmetry allows us to
introduce geometrically a cosmological constant term in four-dimensional $f(R)$
gravity. This symmetry also allows the introduction of a non-vanishing torsion
to the Maxwell $f(R)$ theory. It is found that the antisymmetric gauge field
$B^{ab}$ associated with Maxwell extension is considered as a source of the
torsion. It is also found that the gravitational equation of motion acquires a
new term in the form of an energy-momentum tensor for the background field. The
importance of these new equations is briefly discussed.
