He 'kept/maintained his cool' [=he didn't get angry or upset] even though it was clear that he was being unfairly treated.
He was struggling to 'maintain his cool/composure'. [=he was struggling not to become angry or upset]
They barely had enough food to 'maintain life'. [=to make it possible for life to exist or continue]
(..) and violent dictator. Next! Known for his iconic beard, he is protected by female guards, who he maintains are virgin. Thrust into power at age seven, he may just be the most dangerous man in the entire world. (..)2012 The Dictator