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Hi there.

"We should be obliged if you would send us your catalogue".
I know it refers to Second Conditional and using "would" in if-clause emphasises the politeness of appealing. But... Is it possible for them to send catalogue or it's unreal (because the situation is unreal, the Second Conditional)? would send = sent?

"We shall/would/should be obliged if you will send us your receipts." Here "will" also describes politeness. Can I use any alternatives underlined? It refers to First Conditional, doesn't it? will send = send?

Thank in advance.Emotion: smile
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Use would / would, because it is a polite request and refers to a possible future action. Should (ought to be) is not correct. Shall is used mainly in legal documents today. It is not conditional.
We would be obliged if you would send us your catalogue.

We would be obliged if you sent us your catalogue. (less polite than the above, but that one might be interpreted as being a bit obsequious)

We would appreciate it if you would send us your catalogue. (appreciate is used more in the US than oblige)

We would appreciate it if you would send us your catalogue. (I hear this version more frequently)
We would appreciate it if you could send us your catalogue. (I hear this too, but technically incorrect, it refers to the sender's abililty to send the catalogue)
and very very polite:
We would be most appreciative if...
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Thank youEmotion: smile It's quite odd to call them Conditional, isn' it?

How could we distinguish those in time and possibility? Or all of them are real and refer to the future and just describe politeness?

Any other opinions? Emotion: smile
They are conditional, because the sender has the choice of sending the catalogue or not. Our appreciation is conditioned on what they do.
Would is future. The sentence says that we will be happy if they do send the catalogue. It does not say what we will feel if they do not send the catalogue.
Would is also used in a polite request for someone to do something in the future. The only other choice is imperative, which is not as polite.
Please send us a catalogue. (polite, statement ) Would you please send us a catalogue? (polite request in the form of a question.)
Send us a catalogue, and be quick about it. (imperative, impolite)
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Yes, I got it. Thanks a lot.