Do indexes speed up greater than > comparison in MySQL?

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I have an events tables in my db, which includes among others start_date and end_date columns.

I frequently run queries like

where start_date > 'some starting date' and end_date < 'some end date'

Will I benefit from adding an index to the start_date and end_date columns? I figure out that this is not a = comparison, but maybe anyway.

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