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In case of your parameters there appear underflow and overflow issues, for more on these topics read e.g.: Numerical underflow for a scaled error function

In case of your parameters there appear underflow and overflow issues, for more on these topics read e.g.: Numerical underflow for a scaled error function

Since Mathematica is a really powerful symbolic computing system I recommend a to proceed symbolically as far as we can.

Now Mathematica can evaluate such an integral symbolically:

We have assumed lower limit of integration x0, if we had assumed x0 == 0 the system couldn't provide a symbolic result yielding only an unsatisfactory warning:

Limit[ integral[x0, x, a, b, c, d], x0 -> 0, 
       Assumptions -> {x >= 0, a > 0, b > 0, c > 0, d > 0}]

Now you can solve your equation with Solve providing rational parameters (possibly using appropriate options), otherwise for real parameters use NSolve or FindRoot. Now, it is reasonable to search for numeric solutions since there are Erf functions involved. Your original parameters haven't been justified and it might be necessary it play with AccuracyGoal and PrecissionGoal. E.g. we can easily find the upper limit of integration x these reasonable parameters:

Since Mathematica is a really powerful symbolic computing system I recommend to proceed symbolically as far as we can.

Now Mathematica can evaluate this integral symbolically:

We have assumed the lower limit of integration x0, if we had assumed x0 == 0 the system couldn't provide a symbolic result yielding only an unsatisfactory warning:

area[x_, a_, b_, c_, d_] =
  Limit[ integral[ x0, x, a, b, c, d], x0 -> 0, 
         Assumptions -> {x >= 0, a > 0, b > 0, c > 0, d > 0}]

Now you can solve your equation with Solve providing rational parameters (possibly using appropriate options), otherwise for real parameters use NSolve or FindRoot. Now, it is reasonable to search for numeric solutions since there are Erf functions involved. Your original parameters haven't been justified and it might be necessary it play with AccuracyGoal and PrecissionGoal. E.g. we can easily find the upper limit of integration x for these reasonable parameters:

In case of your parameters there appear underflow and overflow issues, for more on these topics read e.g.: Numerical underflow for a scaled error function

Since Mathematica is a really powerful symbolic computing system I point out a different route to proceed than you seemed to.

Now you can solve your equation with Solve providing rational parameters (possibly using appropriate options), otherwise for real parameters use NSolve or FindRoot.

Since Mathematica is a really powerful symbolic computing system I recommend a to proceed symbolically as far as we can.

Now you can solve your equation with Solve providing rational parameters (possibly using appropriate options), otherwise for real parameters use NSolve or FindRoot. Now, it is reasonable to search for numeric solutions since there are Erf functions involved. Your original parameters haven't been justified and it might be necessary it play with AccuracyGoal and PrecissionGoal. E.g. we can easily find the upper limit of integration x these reasonable parameters:

FindRoot[ area[x, 0.2, 0.3, 6.1, 3.1] == 0.01, {x, 0.5}, 
          AccuracyGoal -> 5, PrecisionGoal -> 5]

{x -> 1.26325}