Answer: Based on your description, I would not recommend filling in the low area in your yard. Rainwater and melting snow create runoff that has to be directed to acceptable areas to collect and soak into the ground, or it has to be channeled through swales or drains so it doesn't flood.
In most yards, there is a drainage pattern created to direct this water away from the house. It sounds like the low area is intended to trap runoff. You would need to provide another place for that water to go. If you fill in the catchment area, the excess water would likely either back up (possibly in an area where it could do damage) or will run off elsewhere (again possibly where it could do damage.) I should mention that in most areas it is illegal to flood your neighbor's property by redirecting runoff.
I would strongly suggest you work with a professionally trained, degreed landscape architect and/or other trained professional with experience in designing drainage systems to determine how best to handle this. I'm sorry I can't be more specific for you long distance.
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