1)Polite request and suggestion..

Would you please give me some advice.

Perhaps it would be helpful for you.

2) reporting future in the past..

She asked if they would help her the next week.

She asked if they would help her moving apartment.

3)  Would can be used in wishes pertaining to the future.

It would have saved time if i had known the procedure well.

Simpe conjugation with auxiliary is often used in polite reuests.

It will work…will it not work?..wont it work?

They will vote for change. Will they not vote for change?  Wont they vote for change?

We will love each other….will we not love each other? Won’t we love each other?

I will work hard..means I am determined to work hard.

They shall work hard. Means they are determined to work hard.

Evolution::: these type of use of will shall is becoming old fashioned in English now.

Bu next December, I all have been living here for three years.

If verb in the main clause in the future tense, then the tense in the subordinate clause would be in present tense.

I will hug you when we meet.

As a result of uncleared instructions, I had been lagging behind the class.

I had been swimming in the confused data.

I had been doing literature search much before he asked us to do.

I had been working on research ideas much before semester started.

Since I had difficulty in following instructor’s little confused instructions in 2011, I had been regretting my decision of choosing the college  all semester when we were assigned the same instructor for the  important course.

Had it not been snowing that day?