@acer 

I took your procedure and implimented it similar to what I mentioned above and that being in a loop, but I was only able to get it to run - as seen in the file - by doing it as presented. 

Is this bad Maple procedure? Is there something less convoluted? This is also a very quick method and I am glad you provided the quick fix. 

Thanks

ErrorRespone.mw

@mmcdara 

Thank you for this respone, I am slightly embarassed I didn't just change the integral myself, I suppose I was wanting to rely on Maple instead of my own brain power. 

Regarding my title, I am interested in running this integral in a doube loop for various values of alpha and b. Since I am doing this the width of this "gaussian" like function will change drastically so I put the bounds as +/- infinity to get the most accurate asnwer. Here is a rough file of what I am interested doing (implimentating your change). 

timeinttest.mw

Thanks

If you have a worksheet you are working with I could respond and help out from there. 

@maryam sadeghi

The figure is extremely small, can you try to edit your post to include a larger sized photo? 

What exactly are you trying to solve here? You are clearly missing an ODE if you have initial condtions, have you tried anything yet? If you post an worksheet with your progress/attempts it may get more responses. 

As well you are defining a function which depends on the functions itself, was that just suppose to be an equal sign? 

Many questions need answers before a viable solution can be attempted. 

@acer Thank you for this thorough explanation.

I am particuarily new to Maple for more sophistcated computations/procedures/code writing so I appreciate this little lesson. Particularily the digits aspect was something I was completely unaware of.

As I will have to do some more complicated computations that are similar to this example I gave I will be make all my further "codes" off of this template. 

Thank you again for all of your help!

@acer 

Thank you for the quick response, and this does exactly what I want, in a very quick way. To answer your inquiry above, yes I am interested in finding the smallest(negative) upon which this inequality is satisfied. 

I knew there was a more efficent way, and what you said about "stopping once found" is what I was interested in doing I was just not sure how to implement in. 

Now for your modification of my procedure, is the time much quicker simply by the way you modified the integral? 

@lemelinm 

This is the downside of my idea.. Interpretation needs to be used. If I find a proper solution I will let you know. 

@acer 

A quick and great response as always. I was unaware of the adaptive option in the plot command, I will keep my eyes out for this in the future.

Much apprecaited.

@ecterrab 

Thank you for this as I now feel embarassed about the simplicity of the problem that I had not considered.

I will forever remember this, and avoid functions with the same names as coordinates if I use this package. 

@Rakshak 

For something to be vacuum means there is zero stress-energy. If the metric itself has unkown function(s) you must solve for those functions before you have the full solution, then the solution will have vanishing Ricci and Einstein tensors. If a metric has unkown functions and is a vacuum solution that is simply stating that you must solve Ricci=0. 

@Jack Zuffante 

If you could upload a worksheet with what you are doing that is the best way to get specific answers to problems you are having. Use the green arrow in top right. 

@acer

A simple fix as I was hoping/assuming, thank you!

@ecterrab 

I am not taking you the wrong way at all. I am aware that my method of comparison is not ideal, I will take fault for that. I was unaware/naive about doing it as simply as you have. But this is where I think the final concern of mine can be seen and probably rectified. 

In your first reponse to my "potential bug" you have in (9) the expression for epsilon=0, a=b=1. Now in your latest post you have either (6) or (7) representing epsilon=0, a=b=1. You can see they do not match, and they should, they are both suppose to be the zeroth order expressions. Now I know we have ignored the physics discussion in this post but I assure you the expression that we obtain will be at most first derivative in both Phi and s. 

If there is something mathematical that I am forgetting and misunderstanding I will admit complete defeat but I am just so surprised that would be the case and that I have not picked that up. I do greatly appreciate your responses and help with post thus far as I have learned way better ways to use the Physics package. 

Edit:  I see your answer with the update you had posted today. Thank you very much for this. 

@ecterrab 

I aggree in that case but the discrepancy in (19) still bothers me. However, consider a different siuation instead. 

Don't let epsilon be zero at the start, instead do subs method for a=b=1 then a series for zeroth order in epsilon they do not agree with what are in the NO_BugMaple_(reviewed).mw file for epslion=0 at the start. Another issue that I think needs to be resolved, because it begs the question with all the options how would one no which is correct? Ofcourse Define is the best approach but requires the most computational time. 

I have attached the issue I described above, sadly I couldn't find a compact way to do it. 

SeriesBug.mw