to make a formal request for something
подавать официальную заявку на что-то (podavat' ofitsial'nuyu zayavku na chto-to)
"I decided to put in for a few days of leave."
"Я решил подать заявку на несколько дней отпуска." (ya reshil put in for neskol'ko dney otpuska)
to do the same set of activities regularly
to perform well despite facing great pressure or challenges
to take action based on advice or feedback
to reduce speed or intensity of work
to exercise at a gym or place regularly
to be full of a strong emotion like happiness or excitement