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

Yes

The word "trabalhei" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese (it is the first-person singular of the pretérito perfeito do indicativo of the verb trabalhar). The only difference is pronunciation. Brazilian Portuguese features more open vowels and a "syllable-timed" rhythm, making the "ei" sound very clear and melodic. Continental Portuguese is "stress-timed" and tends to reduce or "swallow" unstressed vowels, which can make the phonetic realization of the word sound more closed or clipped to a Brazilian ear.

Brazilian Portuguese usage:

1. Eu trabalhei muito ontem. (I worked a lot yesterday.)
2. Trabalhei de casa hoje. (I worked from home today.)
3. Eu trabalhei nessa empresa por dois anos. (I worked at this company for two years.)
4. Eu trabalhei até tarde. (I worked until late.)
5. Trabalhei duro para conseguir isso. (I worked hard to get this.)

Portuguese (Continental) usage:

1. Eu trabalhei imenso ontem. (I worked a lot yesterday.)
2. Trabalhei em casa hoje. (I worked at home today.)
3. Trabalhei nessa empresa durante dois anos. (I worked at this company for two years.)
4. Trabalhei até tarde. (I worked until late.)
5. Trabalhei arduamente para conseguir isso. (I worked arduously to get this.)