What is the expiation for one who fasted Ramadan in previous years without a prior intention to fast the month, or a daily intention for some of its days, and what is the expiation for one who intentionally burped gases that carried a slight taste?

The intention (niyyah) for fasting resides in the heart, and it is not a condition to utter it verbally. Thus, whoever partakes in suhoor (pre-dawn meal) for fasting or if it crosses his mind that he will fast tomorrow, then he has intended. It has not been narrated from the Prophet, peace be upon him, nor from his companions, that they verbally expressed the intention for prayer, purification, or fasting, because it occurs automatically simply by knowing the action. So, if you had suhoor for fasting, you have intended, and you do not need to repeat anything.