The multiple-demand (MD) network is sensitive to many aspects of cognitive demand, showing increased activation with more difficult tasks. However, it is currently unknown whether the MD network is modulated by the context in which task difficulty is experienced. Using fMRI, we examined MD network responses to low, medium, and high difficulty arithmetic problems within two cued contexts, an easy versus a hard set. The results showed that MD activity varied reliably with the absolute difficulty of a problem, independent of the context in which the problem was presented. Similarly, MD activity during task execution was independent of the difficulty of the previous trial. Representational similarity analysis further supported that representational distances in the MD network were consistent with a context-independent code. Finally, we identified several regions outside the MD network that showed context-dependent coding, including the inferior parietal lobule, paracentral lobule, posterior insula, and large areas of the visual cortex. In sum, cognitive effort is processed by the MD network in a context-independent manner. We suggest that this absolute coding of cognitive demand in the MD network reflects the limited range of task difficulty that can be supported by the cognitive apparatus.