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I wonder why the modal verb comes at the end here?

..., die die Produktivität des Programmierers erhöhen soll.

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    Your citation seems to be incomplete. Can you quote the complete sentence, please? – tofro Feb 18 at 21:40
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    I don't understand the somewhat reflexive close-votes. True, it is not a very well asked question, but a competent speaker of german will know what the questioner wants to know. So voting to close because of it is unclear what you are asking is somewhat fogeyish in my humble opinion. – jonathan.scholbach Feb 18 at 22:06
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That is because the snippet you posted is a dependent clause. It explains something in the main clause. Dependent clauses have their conjugated verb in the last position in German.

Agile Softwareentwicklung ist eine Methode, die die Produktivität des Programmierers erhöhen soll.

The first die isn't an article but a relative pronoun. Der/die/das often replaces the pretty clunky welcher/welche/welches relative pronoun.

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    +1, esp. for the (successful) effort of trying to understand what the questioner probably wanted to know instead of a somewhat knee-jerk approach to close the question. – jonathan.scholbach Feb 18 at 22:04
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Your question has nothing to do with modal verbs. In any subordinate clause the verb is placed at the end.

On the site of the University of Michigan you find:

III. Where to position the verb in the relative clause

This is easy also: relative clauses are subordinate clauses. Consequently, the conjugated verb comes at the end of the relative clause.

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