There are several synonyms for the phrase "without becoming upset." Some examples include "calmly," "serenely," "composedly," "tranquilly," "stoically," and "peacefully." These words suggest a sense of control and a lack of emotional turmoil or agitation. Choosing the right synonym can help convey a particular tone or mood in writing or speech. For instance, if you want to portray someone who is unperturbed in the face of adversity, you might use "stoically." Alternatively, if you want to imply a more relaxed or meditative state, you could opt for "peacefully." Ultimately, using synonyms can add nuance and depth to language and help us convey our thoughts and feelings more precisely.