select * from( (SELECT * FROM table WHERE ST_Intersects(geomfromtext( 'POLYGON((
$rectanglePoint1X $rectanglePoint1Y, $rectanglePoint2X $rectanglePoint2Y,$rectanglePoint3X
$rectanglePoint3Y,$rectanglePoint4X $rectanglePoint4Y,$rectanglePoint1X $rectanglePoint1Y))') , geomfromtext( 'POLYGON((
$polygonPoint1X $polygonPoint1Y, $polygonPoint2X $polygonPoint2Y,$polygonPoint3X
$polygonPoint3Y,$polygonPoint4X $polygonPoint4Y,$polygonPoint1X $polygonPoint1Y))')))
union(SELECT * FROM usgs_data_repo WHERE ST_Contains(geomfromtext( 'POLYGON((
$rectanglePoint1X $rectanglePoint1Y, $rectanglePoint2X $rectanglePoint2Y,$rectanglePoint3X
$rectanglePoint3Y,$rectanglePoint4X $rectanglePoint4Y,$rectanglePoint1X $rectanglePoint1Y))') , geomfromtext( 'POLYGON((
$polygonPoint1X $polygonPoint1Y, $polygonPoint2X $polygonPoint2Y,$polygonPoint3X
$polygonPoint3Y,$polygonPoint4X $polygonPoint4Y,$polygonPoint1X $polygonPoint1Y))')))
union(SELECT * FROM usgs_data_repo WHERE ST_Contains(geomfromtext( 'POLYGON((
$polygonPoint1X $polygonPoint1Y, $polygonPoint2X $polygonPoint2Y,$polygonPoint3X
$polygonPoint3Y,$polygonPoint4X $polygonPoint4Y,$polygonPoint1X $polygonPoint1Y))'),geomfromtext( 'POLYGON((
$rectanglePoint1X $rectanglePoint1Y, $rectanglePoint2X $rectanglePoint2Y,$rectanglePoint3X
$rectanglePoint3Y,$rectanglePoint4X $rectanglePoint4Y,$rectanglePoint1X $rectanglePoint1Y))') )))
where { $rectanglePoint1X $rectanglePoint1Y, $rectanglePoint2X $rectanglePoint2Y,$rectanglePoint3X
$rectanglePoint3Y,$rectanglePoint4X $rectanglePoint4Y} are the co-ordinates of the rectangle(Input 1)
and {$polygonPoint1X $polygonPoint1Y, $polygonPoint2X $polygonPoint2Y,$polygonPoint3X
$polygonPoint3Y,$polygonPoint4X $polygonPoint4Y} are the co-ordinates of the polygon(Input 2)
Note that the above code will work in the case of any polygon instead of a rectangle as Input1