When I try not to look anxious, I don't think I look anxious. I do remember one time we had a lock down in school and the teacher told me I looked the least worried and was the calmest one there. I really wasn't anxious about the gun in our school, but was still quite uncomfortable about all the people around to talk to.
I think I look more uncaring, or indifferent, about things. I smile, but I don't look sincerely phased by things. Some people take this as depression, others take it as mellowness.