f1 := 1.002*S +0.004002*S^2 +3e-06*S^3;

NiM+SSNmMUc2IiwoSSJTR0YlJCIlLTUhIiQqJEYnIiIjJCIlLVMhIicqJEYnIiIkJEYxRi8=

f2 := 1 1.002*S +0.002001*S^2 +1500*S^3;

NiM+SSNmMkc2IiwqJCIjOiEiIiIiIkkiU0dGJSIlLjoqJEYrIiIjJCImOiskRikqJEYrIiIkIiUrOg==

f3 := ;

NiM+SSNmM0c2IiwqSSJTR0YlISQsJiokRiciIiMkIiYwKyIhIiIqJEYnIiIkIiUrOiQhIzpGLSIiIg==

solve (f3, S);

NiUkISIiIiIhJCIrJipSd2ZMISM1JCErUCYqUndIISM3

plot (f3, S=0..1);

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

f4 := f1/(1+1002*S + 2001*S^2 + 1000*S^3);

NiM+SSNmNEc2IiomLChJIlNHRiUiJS01KiRGKCIiIyIlLVMqJEYoIiIkIiUrSSIiIiwqRjBGMEYoRilGKiIlLD9GLSIlKzUhIiI=

plot (f4, S=0..0.01);

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

plot (f4, S=0.01..3.9);

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

f5 := (1002*S + 2*500001*S^2 +1.875e08*S^3)/(1+1002*S+ 500001*S^2 + 6.25e07*S^3);

NiM+SSNmNUc2IiomLChJIlNHRiUiJS01KiRGKCIiIyIoLSsrIiokRigiIiQkIiV2PSIiJiIiIiwqRjJGMkYoRilGKiInLCtdRi0kIiREJ0YxISIi

solve (f5-1.5,S);

NiVeJCQhKyJlW2dfIyEjNyQhKyx3I1FyJiEjOF4kRiQkIissdyNRciZGKSQiK2leVSZRI0Ym

plot (f5, S=0..0.019);

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