@PedroTamaroff I am trying to deform $k[x]$ to a curved dg-algebra with trivial differential but non-trivial curvature and then compute its Hochschild cohomology. In this case I'm afraid that the Koszul resolution doesn't work so we have to stick to the original definition. Hence I am curious how to compute the Hochschild cohomology of $k[x]$ through the original definition.
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