Is the word problemas the same in Brazilian and European Portuguese?

Yes

The spelling, meaning, and grammatical function of "problemas" are identical in both Brazilian and Continental Portuguese. The only difference lies in pronunciation:

• Brazilian Portuguese: The pronunciation is generally "open," with clearly articulated vowels and a more melodic, syllable-timed rhythm.
• Continental Portuguese: The pronunciation features heavy "vowel reduction." Unstressed vowels are often shortened or nearly swallowed, making the word sound more "consonantal" and clipped.

Brazilian Portuguese Examples:

1. "Eu estou com muitos problemas no trabalho." (I am having many problems at work.)
2. "Você está com algum problema?" (Are you having some trouble?)
3. "Não vai dar problema nenhum." (It won't cause any trouble at all.)
4. "Meu celular está dando problemas." (My cell phone is having problems/acting up.)
5. "A gente tem muitos problemas para resolver hoje." (We have many problems to solve today.)

Continental Portuguese Examples:

1. "Estou a ter alguns problemas no trabalho." (I am having some problems at work.)
2. "Não há problema nenhum nisso." (There is no problem at all in that.)
3. "Tivemos problemas com o carro ontem." (We had problems with the car yesterday.)
4. "Isso pode causar problemas à nossa equipa." (That can cause problems to our team.)
5. "Ele gosta de criar problemas desnecessários." (He likes to create unnecessary problems.)