Shana and From the New World were mentioned above, which I'd definitely agree (both are strong and mostly independent, and pretty low on obscenity and fanservice like you asked for).
Apart from those, the ones I'd recommend most are my Top 2, Steins;Gate and Cowboy Bebop. Two of the best anime ever, Faye Valentine from the latter is both well-written and falls into most of your criteria (though she's by no means the badass Spike is) and though Steins;Gate isn't much of an action anime (sci-fi thriller), Makise Kurisu is easily the smartest character in the series and more often than not aids her male counterpart rather than the reverse.
And, of course, a conversation about strong females isn't complete without Major Kusanagi from Ghost in the Shell.
It's a pretty confusing storyline, but the characters are great and the animation still holds up beautifully.
Apart from those, the ones I'd recommend most are my Top 2, Steins;Gate and Cowboy Bebop. Two of the best anime ever, Faye Valentine from the latter is both well-written and falls into most of your criteria (though she's by no means the badass Spike is) and though Steins;Gate isn't much of an action anime (sci-fi thriller), Makise Kurisu is easily the smartest character in the series and more often than not aids her male counterpart rather than the reverse.
And, of course, a conversation about strong females isn't complete without Major Kusanagi from Ghost in the Shell.
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