To present an extreme example to emphasize the surprising degree.
例:
1. 冷蔵庫には卵さえ入っていない。
There aren't even any eggs in the refrigerator.
2. 旅好きな彼は北極にさえ行ったことがある。He, an avid traveler, has even been to the North Pole.
3. 学者でさえ解けない問題が試験に出たA problem that even scholars couldn't solve appeared on the exam.
To indicate the bare minimum required.
例:
1. 自分さえよければ、それでいいのですか。
Is it all right as long as only you are okay with it?
2. 雨さえ降らなければ、花火ができる。As long as it doesn't rain, we can have fireworks.
3. 人に道を聞きさえすれば、迷子にならないよ。If you just ask someone for directions, you won't get lost.