Why should I disbelieve her story?

我为什么要怀疑她的说法呢？

《牛津词典》

Why should I apologize?

我为什么要道歉？

《牛津词典》

To whom should I write?

我应该把信写给谁？

《牛津词典》

What should I do? But,the telephone rang, and I forgot the problem for the time being.

VOA: special.2011.06.04

So what should I do? Actually I lied, by the way, when I said the answer was over there.

我应该怎么做呢，实际上当我说答案,在那儿的时候我撒谎了。

麻省理工公开课 - 计算机科学及编程导论课程节选

And if you talk to most Americans and you're like, "Oh, why should I put this article there?"

如果你这样问大多数美国人，“为什么要把这个冠词放在这儿？”

韩国人经常犯的失误 - SpeakingMax英语口语达人

Should I recognize all of the unrealized capital losses I have now, before the end of 2010?

FORBES: Don't Rush To Recognize Capital Gains Or Losses

Why should I believe it should be 65 cents when you've been so conservative?

FORBES: Magazine Article

In the morning: Should I dry my hair or just run out with wet hair?

FORBES: The Right to Choose: Work and Motherhood