Answer: This is actually a very complex question and it is beyond the scope of this simple Q&A to give you an accurate and useful answer. Deciding what to do must take into account the overall drainage pattern and runoff capacity of the overall area that drains to that spot, as well as look at the consequences of your changes downstream. It may be that area was designated as a catchment area to allow water to gradually soak into the ground and thus is functioning as designed. In general, filling is not a good idea in the long run because the water has to drain somewhere -- and filling can cause it to back up at an even less desirable location; it is also usually illegal (not to mention unfriendly) to flood your neighbor. I would strongly suggest you work with a landscape architect or other professionally trained expert with experience in grading issues and explore your options. I'm sorry I can't be more specific for you but I hope this helps you begin to understand the issues.
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