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There most be a thousand SF novels and short stories out there that feature super-intelligent characters. Read as many of them as possible.
I think you need to come up with the proverbial "kryptonite" so to speak. What problems would be solved with a higher functioning mind and which problems might be accentuated? Certainly, most high-function protagonists tend to suffer from boredom without challenges, so the obvious answer is to keep them asking, learning and moving forward. With Sci-fi you can add the unknown and unexplained into the mix to keep the fires stoked. I think that could be a source of frustration for a character that may be accustomed to having all the answers is to create situations that involve phenomena that they are unable to process using traditional scientific dogma (i.e. magic). You could also have significant character flaws that despite their great intellegence, they are lacking in a number of areas that a "lesser" human could excel in.
This notion of "drive and curiosity" seems a bit circular. Are we to assume that if an intelligence "gets things done" then it must have had what we would understand as "drive and curiosity"? Suppose an intelligence had the aim of not getting anything done, ie it devotes its drive and curiosity to ensuring that nothing gets done?
This could be read as the drive of some of the AIs in Banks culture novels -- elaborate efforts not to interfere with non-machine doings as much as possible. As Banks sees it, such machines would devote most of their drive and curiosity to internal simulations. There would be no sign of things getting done and no sign of any drive and curiosity.
In the Novel Excession there are borderline cases of drive and curiosity going into events verging on the not-getting anything done (the machine that harbors sleepers and simulates old wars and the machine that digs up past genocides to use to torment the genocidal). Other machines mock them since they have the morally superior position (for a Banks AI) of not having gotten anything done at all.