An important unsolved problem is how the brain survives in a complex world by performing a rich repertoire of computation on a minimal energy budget. Despite using a seemingly fixed architecture, the brain performs much better than current generations of computers and artificial intelligence. Neuromodulation is updating the effectiveness of signal transmission, giving rise to variable effective connectivity between regions to allow computational richness. Here, we integrate 19 empirical neurotransmitter maps as modulators of the underlying local regional dynamics in a whole-brain model of human brain activity. Our neurotransmission-modulated (NEMO) framework flexibly computes different tasks. For each individual, "brain computability" is defined as the ability to fit all tasks. Brain computability correlates with behavioral performance on individual tasks and with a general behavioral measure of intelligence. Overall, NEMO sculpts brain dynamics in a fixed brain architecture to compute the rich repertoire of tasks required for surviving and thriving.