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]
(..) - You can...? - Yes. We're allowed that privilege. Some more of this? It is called wine. There are thought criminals who maintain that the Resistance is not real. Believe me, Winston, it is very real. Perhaps you are not familiar with how it operates. I'm attentive to the news. Indeed. (..)1984 1984