textbook on the human brain for computer scientists/machine learning professionals? The human brain as studied by neuroscientists, or neurobiologists, generally focus on what I would call 


implementation details (how specifically does information transport between synaptic channels, i.e. what are the chemical processes)
vague generalities (e.g. about "memory" as a psychological concept and in very vague terms what types of memory there are without studying them mathematically)


There is nothing intrinsically wrong with this.

But I am interested in the brain as a computational system. Of course we don't yet understand the brain very well, but is there a book on the brain that a computer scientist or machine learning professional could read to get a computational/systematic understanding of what we know about the brain? e.g. what is the computational role of various neurotransmitters (without going into chemistry), etc.
There is no "textbook" on this. However, there is a book! It is How to Create a Mind by Raymond Kurzweil, the director of engineering at Google. Excellent book that explains the brain from a computer-science perspective. It goes into a lot of detail.

Check out the intro sound bytes on Audible.

For a closer to the metal (i.e. actual implementations of models of the brain), check out Cognitive Architectures, such as ACT-R, Soar, CLARION, ICARUS, EPIC, LIDA, etc. Here is a survey.