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]
(..) How right you are. Which is why I developed this inhibitor chip... ...to protect my higher brain function. It means I maintain control of these arms, instead of them controlling me. And now on to the main event. Give me the blue light, Rosie. Precious tritium is the fuel that makes this project go. (..)2004 Spider-Man 2
(..) You might want to... Can I help you? Yeah, I've come to see the show. Oh, I'm sorry, sir. No one will be seated after the doors are closed. It helps maintain the illusion. Miss Watson, she's a friend of mine. She asked me to come. But not to come late. I have to see this show. (..)2004 Spider-Man 2