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 tell... lies, Dad. You tell amusing lies. Stories are what you tell a -year-old at bedtime. They're not elaborate mythologies that you maintain... ...when your son is and and and . And I believed you. I believed your stories so much longer than I should have. (..)2003 Big Fish