Translating "should" to express what is probable or expected I've struggled with this for a while, and I haven't found a definitive answer. In English we can use 'should' to indicate an estimation or probability.
Merriam-Websters 4th definition is that should

is used in auxiliary function to express what is probable or expected

For example:

He should be here by 7PM.
I should have it done by Friday.
It should run in Windows 95.

I use 应该 but it feels wrong since there is no sense of obligation or demand, whereas there is such a connotation in &quot;should&quot;. What should I use?
Generally, you can use 应该. However, as Stan says in comments, it does carry the connotation that there is some reason why it "should" be. So, for example, you could say a sentence like:

[要是他六点离开了，]他应该七点到。
[If he has left at six, ] he should be here at seven.


If you're just throwing out an estimate, it would be better to use an "I think..." construction. This carries less of a tone of uncertainty than it does in English:

我认为我周五会把这个任务办好。
I think I'll have it done by/on friday.