  Rota-Baxter systems are modified by the inclusion of a curvature term. It is
shown that, subject to specific properties of the curvature form, curved
Rota-Baxter systems $(A,R,S,\omega)$ induce associative and (left) pre-Lie
products on the algebra $A$. It is also shown that if both Rota-Baxter
operators coincide with each other and the curvature is $A$-bilinear, then the
(modified by $R$) Hochschild cohomology ring over $A$ is a curved differential
graded algebra.
