(humble) my manuscript

proofreading and correction / calibration

to proofread and correct / to calibrate

petition (the honorific form of 願い)

used as the word for please, familiar honorific.

Please (emphasize a request).

please think well of me, please take care of me (a newstarter after an introduction) / please take care (of) (when entrusting a person or piece of property to someone)

(humble, formal, polite) Please (do). Humble form of お願いします (onegai shimasu).