Crossword Genius

Very keen, free to generate capital (6)

Ross

I believe the answer is:

madrid

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'capital' is the definition.
(capital of Spain)

'very keen free' is the wordplay.
'very keen' becomes 'mad' (I've seen this in other clues).
'free' becomes 'rid' (to be free of something is to be rid of it).
'mad'+'rid'='MADRID'

'to generate' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for madrid that I've seen before include "Capital of Spain since 1561" , "Spanish city" , "City with the Prado national art gallery" , "Spanish capital" , "Spain's capital" .)

I've seen this clue in The Sun.
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